尔雅Discrete Mathematics答案(学习通2023课后作业答案)

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1. Propositional logic of mathematical logic

Chapter 1 unit tests

1、尔雅Which is 答答案a proposition in the following statements?
A、Please don't copy!
B、案学The习通 sun is a planet.
C、Can I smoke here?课后
D、x – y = 3

2、作业Which is 尔雅an atomic statement in the following statements?
A、Zhang San and LiSi are friends.
B、答答案If it rains tomorrow,案学 I won't go to the park.
C、The习通re is no savior or god.
D、Xiao Ming is 课后either in class or running on the playground.

3、Suppose P: I'm Chinese Q: I come from Beijing "Unless I am from Beijing,作业 I am not Chinese" is the result of the symbolic statement:
A、
B、尔雅
C、答答案
D、案学

4、Which is a false statement in the following statements?
A、When x >4, then x+1 > 5
B、As long as today is the Spring Festival, tomorrow is the Lantern Festival.
C、If the earth does not turn, the crow is white.
D、2 is a prime number only if USTB is not in Beijing.

5、Which is the simplified form of the following combination formulas:?
A、
B、
C、
D、

6、According to the implication law, which one is equivalented in the following formulas？
A、
B、
C、
D、

7、German Nazi leader goebbels once said that a lie repeated three times becomes a truth.Which law does this violate?
A、Law of double negation
B、Idempotent law
C、Associative law
D、DE Morgan law

8、"Stinky tofu stinks and smells good" is a false statement.Which law does this use?
A、Law of identity
B、Law of excluded middle
C、Law of contradiction
D、Absorption law

9、Our cat either sleeps on the balcony or eats meat in the kitchen.I haven't found it on the balcony yet, so it must be in the kitchen.What is the law of inference used?
A、Modus tollens
B、Refuse to take type
C、Disjunctive syllogism
D、Structural difficulty

10、What is the dual of?
A、
B、
C、
D、

11、What is the type of?
A、tautologies
B、contradiction
C、Nontautological satisfiable formula
D、Unable to determine

12、Which one is conjunctive and disjunctive paradigms?
A、
B、
C、
D、

13、Which are propositions in the following statements?(multiple choices)
A、The shot is not a ball.
B、If he doesn't play, we'll lose.
C、Liu xiang spent less than 13 seconds in the 110m hurdles. Does he a real athlete?
D、Liu xiang took less than 13 seconds in the 110m hurdles. He is a real athlete.

14、Which are not compound propositions in the following propositions? Multiple choices
A、I can't sing.
B、If it doesn't rain,I'll go out.
C、I have classes every day.
D、Are there people on Mars?

2. Predicate logic of mathematical logic

Chapter 2 unit tests

1、Which one is not a predicate formula?
A、
B、
C、
D、

2、In the formula，the free variable is()
A、第一个x
B、第二个x
C、y
D、z

3、Which one is wrong?
A、
B、
C、
D、

4、Which one is wrong?
A、
B、
C、
D、

5、Which one is wrong?
A、
B、
C、
D、

6、There is a proposition as follows: any real number x, there will always be real number y, which is less than x. Set: F(x): x is a real number. G(x, y) : x < y What is the symbolic representation of the correctness of the proposition in the scope of predicate logic?
A、
B、
C、
D、

7、Which one is the prenex normal form?
A、
B、
C、
D、

8、Suppose the individual domain is a set of integers. Which has a true value of 0 in the following formulas?
A、
B、
C、
D、

9、Which is correct in the following formula?
A、
B、
C、
D、

10、Which is not the Negation of formula?
A、
B、
C、
D、

11、The type of well-formed formulais Tautology

12、Set the individual domain { 1,2}, the predicate P (1) = 1, P (2) = 0, Q (1) = 0, Q (2) = 1,so the truth-value ofis 1.

13、The type of formulais Tautology

14、Let the individual domain be A = { a, b}, The formulaafter eliminating the quantifier should be.

15、Determine whether this formula is correct:

3. Set of set theory

Chapter 3 unit tests

1、The cardinal numbers of which set is three?
A、
B、Null set
C、
D、{ x | x是选修北京科技大学离散数学慕课的人}

2、What’s wrong?
A、
B、
C、
D、

3、Which of the following is wrong ?
A、
B、
C、
D、

4、On [1, 100], how many integers can't be divided by 3 and 5 or 7?
A、45
B、27
C、33
D、62

5、A. B and C are arbitrary sets. What's right?
A、
B、
C、
D、if,then

6、A. B is any set. What's the error?
A、
B、
C、
D、

7、A. B and C are arbitrary sets. What's right?
A、
B、
C、
D、

8、Known ,what the method of solving the order of the value of and ?
A、
B、
C、
D、

9、Due to ,what can be deduced?
A、
B、
C、
D、

10、What laws are used in the following reasoning?
A、Law of identity
B、Law of distribution
C、Law of zeros
D、Commutative law

11、

12、Suppose a, B and C are any set,

13、

14、

15、

16、Suppose a, B and C are non null sets,ifand,then.

4.Binary relation of set theory

unit test of binary relation

1、Which of the follwing has the Transitive relationship?
A、father-son relationship
B、The same year relationship of ancient imperial examination
C、Relations with neighboring countries
D、The relationship between taking the same course

2、Which of the following is equivalent?
A、The division relation on the set of integers
B、On the set of rational numbers, the relation of multiplication equal to 1
C、rank relationship
D、Logical equivalence of propositional formula

3、A. B, C and D are arbitrary sets. What’s right?
A、
B、
C、
D、

4、What’s right?
A、The poset of a finite set must have the largest element
B、The poset of a finite set must have the Maximal element
C、Covering relation is partial order relation
D、The maximum and minimum elements of a finite set must be different

5、R is a binary relationship, and , which of the following is not necessarily transitive?
A、
B、
C、
D、

6、There are 255 binary relations on a = { 1, 2, 3, 4, 5}

7、A = { a, b}, R is the relationship on A, r = { < a, a >, < b, b >}, then R is not transitive.

5. Functions of set theory

functional unit test

1、Considering the function on the real number set, the analytic expression of is
A、
B、
C、
D、

2、Which of the following relationships can form a function?
A、f={ <x, y>| x,y∈N, and x+y<10}
B、f={ <x, y>| x,y∈R, and y2=x}
C、f={ <x, y>| x,y∈N, and Y is the number of prime numbers less than x}
D、f={ <x, y>| x,y∈N, and x2+y2=1}

3、Which of the following functions has an inverse function?
A、f:Z->N, f(x)=x2
B、f:Z->N, f(x)=|x|
C、f:N->Z, f(x)=x
D、f:N->N, f(x)=x

4、Suppose A and B are finite sets,|A|=n，|B|=m，and n,m>0，then
A、
B、
C、
D、

5、Which of the following statement is correct ()
A、A and B are two equal sets. The function from A to B is unijection only if it is a hyperjection.
B、The inverse relations of functions are not always functions.
C、Only bijective function is invertible, and its inverse function is bijective.
D、The composition of a function is not necessarily a function.

6、The number of elements in set A is n, and the number of elements in set B is m. The different surjections from set A to set B are equal to the number of m-containing elements in set A of n elements.

7、The number of elements of set a is n, and the number of elements of set B is m. There are m*n kinds of different bijections from set a to set B.

7.Algebraic system of algebraic structure

unit test of algebra system

1、Let G be a non-zero real number set R * for the algebraic system composed of ordinary multiplication, which of the following functions is the endomorphism of G?
A、f(x) = |x|
B、f(x) = |x| +1
C、f(x) = 0
D、f(x) = 2

2、Which of the following is not a binary operation on the integer set Z?
A、division
B、addition
C、subtraction
D、multiplication

3、On the natural number set N, which of the following operations can be combined?
A、a*b=max{ a,b}
B、a*b=a-b
C、a*b=a+2b
D、a*b=|a-b|

4、Let A = { 2, 5, 8}, the binary operation * is defined as: a * b = max { a, B}, then the unit element in < A, * > is
A、2
B、non-existent
C、5
D、8

5、Let A = { 2,5,8}, the binary operation * is defined as: a * b = max { a, b}, then the zero element in < A, * > is
A、8
B、non-existent
C、2
D、5

6、Let A = { 2, 5, 8}, the binary operation * is defined as: a * b = min { a, b}, then in < A, * > the unit element is
A、8
B、non-existent
C、2
D、5

7、Let A = { 2, 5, 8}, the binary operation * is defined as: a * b = min { a, b}, then in the unique point < A, * > the zero element is
A、2
B、non-existent
C、5
D、8

8、Q is the rational number set N, and the definition operation * on Q is a*b= a + b – ab, then the unit elements of <Q, * > is
A、0
B、a
C、b
D、1

9、Let v = < Z, + > and which of the following functions is the endomorphism on V?
A、f(x)=5x
B、f(x)=x+5
C、f(x)=|x|+5
D、f(x)=x*x

10、Let G1=<{ 0,1,2},°>，G2=<{ 0.1},*>,where °denotes modulo 3 addition, * denotes modulo 2 multiplication, then the unit element of product algebra
A、<0,1>
B、<0,0>
C、<1,0>
D、<1,1>

11、The following sets are subsets of N, which of the sets are closed under normal addition operations
A、{ x | X is a multiple of 30}
B、{ x|The power of X can be divided by 16}
C、{ x|X and 5 mutual quality}
D、{ x|X is a factor of 30}

12、On the natural number set n, which of the following operations are commutative?
A、a*b=max{ a,b}
B、a*b=|a-b|
C、a*b=a-b
D、a*b=a+2b

13、Which of the following is a binary operation on n?
A、addition
B、multiplication
C、subtraction
D、division

14、Which of the following is not a binary operation on n?
A、subtraction
B、division
C、addition
D、multiplication

15、V=<R*,×>, which of the following functions are homomorphisms of V to v?
A、f(x)=x*x
B、f(x)=1/x
C、f(x)=2x
D、f(x)= -x

16、In the operation table, if the element arrangement order of the row and column where an element is located is consistent with that of the header element, then this element is the unit element.

17、In an operation table, if the elements of an element's row and column are the element itself, then the element is zero.

18、If the elements of the operation table are symmetrically distributed about the main diagonal, the operation can be combined.

8. A Preliminary Study of Group Theory of Algebraic Structure

preliminary unit test of group theory

1、Any subgroup of a finite group of order 6 must not be()
A、Rank 4
B、Rank 2
C、Rank 3
D、Rank 6

2、Let a be the generator of group of order 10, then the fourth power of a is the element of order ().
A、Rank 5
B、Rank 10
C、Rank 4
D、Rank 6

3、Let a be the generator of group of order 10, then the third power of a is the element of order ().
A、Rank 10
B、Rank 5
C、Rank 4
D、Rank 6

4、Let a be the generator of group of order 12, then the second power of a is the element of order ().
A、Rank 6
B、Rank 12
C、Rank 5
D、Rank 4

5、Let a be the generator of group of order 12, then the third power of a is the element of order ().
A、Rank 4
B、Rank 12
C、Rank 5
D、Rank 6

6、If <G,*> is a group, then * is()
A、Have identity element and can be combined
B、Satisfy the law of Union and the law of exchange
C、Have identity element and satisfy the law of exchange
D、Have inverse, zero element

7、The order of a subgroup of a sixth order group can be
A、2,3
B、1,2,5
C、2,4
D、3,6,7

8、Let K = { e , a , b , c}, < K, * > is a Klein quaternion group, then the inverse element of element a is
A、a
B、e
C、b
D、c

9、The subgroups of group < Z4, ⊕ > is
A、<{ 0,2},⊕>
B、<{ 0,1},⊕>
C、<{ 0,3},⊕>
D、<{ 0,1,3},⊕>

10、Which of the following in algebraic systems <S,*> is a group?
A、S={ 1，3，4，5，9}，* is module 11 multiplication
B、S={ 0，1，3，5}，* is modulo 7 addition
C、S = Q (set of rational numbers), * is a common multiplication
D、S = Z (integer set), * is a common subtraction

11、If S={ 0，1}, * is a normal multiplication, then < S , * > is
A、It's just a monoid , but not a group
B、Semigroup,but not a monoid
C、group
D、Ring,but not a group

12、Binary operation * defined on rational set Q.If any rational number x, y has x * y = x + y-xy, then q satisfies
A、If any rational number x, x is not equal to 1, there is inverse element
B、All elements have inverse elements
C、Only one inverse element
D、All elements have no inverses

13、Which of the following are generators of cyclic group < a > of order 8 ?
A、a
B、The third power of a
C、The fifth power of a
D、a的7次幂

14、Which of the following are subgroups of cyclic group <a> of order 8?
A、{ e}
B、<a>
C、Groups generated by the power of 4 of a
D、Groups generated by the power of 2 of a

15、Which of the following are nontrivial subgroups of cyclic group < a > of order 8?
A、Groups generated by the power of 4 of a
B、Groups generated by the power of 2 of a
C、{ e}
D、<a>

16、If <G,*> is a group, then * is()
A、Satisfied combination law
B、Have Unit element
C、Every unit has inverse element
D、Exchangeable

17、In a group 〈G,*〉, if the order of element a in G is k, then the order of the inverse element of a is -k.

18、Groups of prime order must be cyclic groups.

19、The number of elements of order 2 in even order groups must be odd

20、The number of elements with order greater than 2 in a finite group must be even.

21、There is no zero element in a group with at least two elements.

22、a is the generator of a group〈G，*〉, then the inverse of a is also the generator of a group〈G，*〉.

23、There must be an element of order 2 in an even order group.

24、Group G has no idempotent except unit element.

10. The basic concept of graph in graph theory

basic concept unit test of Graphs

1、If G is a self complementary graph of order n, what the edge numbers of G?
A、n(n-1) / 4
B、n / 2
C、n / 4
D、n(n-1) / 2

2、If undirected graph G has 16 edges, 3 4-degree nodes, 4 3-degree nodes, and the degrees of other vertices are less than or equal to 2, how many vertices are there at least in G?
A、11
B、12
C、15
D、16

3、Now there are n boxes. If there is exactly one ball of the same color in each of the two boxes, and there are exactly two balls of each color, and they are put in different boxes, how many different colors are the balls in these n boxes?
A、n(n-1) / 2
B、n / 2
C、n
D、n(n-1)

4、What’s right?
A、Graph isomorphism is an equivalent relation
B、The sequence of nonnegative integers (5,4,3,2,2) can be simplified graphically
C、In any directed graph, the sum of the in-degree of all vertices is not equal to the sum of the out-degree of all vertices
D、The sequence of nonnegative integers (3, 3, 3, 1) is not graphical

5、What’s right?
A、In any graph, the sum of degrees of vertices is equal to twice the number of edges.
B、The necessary conditions for isomorphism of two graphs are equal order, equal edge number and equal degree sequence.
C、A graph with a given point or edge weight is called a weighted graph.
D、A graph with specified symbols for both vertices and edges is called a calibration graph.

6、In a graph, there are both directed and undirected edges. Such a graph is called a mixed graph. Is that right?

7、A simple graph in which all vertices have the same degree is called a regular graph. Is that right?

11. Connectivity of Graph Theory Graphs

connectivity unit test of Graphs

1、In graph G, the distance D (U, V) from vertex u to V does not satisfy which of the following properties?
A、d(u, u) = ∞
B、d(u, v)≥0
C、d(u,v) = d(v,u)
D、d(u,w)+ d(w ,v) ≥ d(u,v)

2、In undirected graph G = < V, E > is the connected relation between vertices on V?
A、equivalence relation
B、Partial order relation
C、Compatible relationship
D、Identity relationship

3、What is wrong with the following statement?
A、If an edge in an undirected graph is a cut edge, it must be included in any simple circuit in the graph.
B、A directed graph is a unilateral connected graph only if there is a path through each vertex at least once.
C、Every vertex and every edge of a simple digraph lies exactly in a weak partition graph.
D、A directed strongly connected graph, only if there is a circuit and it contains every vertex at least once.

4、What is the number of edges in a connected graph with n vertices?
A、At least n-1.
B、Up to n-1.
C、Up to n.
D、At least n.

5、which of the following statements are true?
A、If all the vertices in a path are different, the path is called the basic path.
B、If a vertex of a connected undirected graph is a cut point of the graph, it must be a joint point of a pair of vertices.
C、If any pair of vertices are reachable to each other, then this graph is a strongly connected graph.
D、If a graph is connected on one side, it is called weak partition graph.

6、which of the following statements are true?
A、A digraph G is strongly connecte only if there is a loop in G, it passes through every vertex at least once.
B、A directed graph is a one-way connected graph if and only if it has a path through all nodes.
C、In G=<V,E> with n vertices, if there is a path from u to V, there must be a path shorter than n-1 from u to v.
D、Let the vertex number n = 7 and the edge numbers of M = 10 in a simple plane graph G, then G is connected.

7、If there is a path between two vertices, the path between the two vertices is still obtained by deleting part of the path between repeated vertices on the path, and the length is less than the number of vertices in the graph. Is this statement correct?

8、Let n be the number of vertices of a connected simple undirected graph, and K be the minimum degree of vertices in the graph. Then, if there must be a basic path with a length of 2K in the graph?

12. Matrix Representation of Graph Theory Graphs

graph theory and matrix representation unit test of Graphs

1、It is known that the adjacency matrix of a digraph D is as follows. The nodes corresponding to the matrix are v1 to v4 from left to right. How many paths are there in D with the length of 3 from v1 to v4?
A、2
B、1
C、3
D、4

2、The reachability matrix of a digraph is known as follows,the graph is a ( )?
A、Unilateral connected graph
B、Strongly connected graph
C、Weakly connected graph
D、Unconnected graph

3、Given that the correlation matrix of a simple digraph is as follows, which of the following pairs of nodes are reachable to each other?
A、v3, v4
B、v1, v2
C、v2, v3
D、v4, v1

4、What is wrong with the following statement?
A、A digraph is a unilateral connected graph only if all elements of the reachable matrix are 1.
B、Undirected graph is connected graph if and only if all elements of its reachable matrix are 1.
C、A digraph is a strongly connected graph only if all elements of its reachable matrix are 1.
D、A digraph is a weakly connected graph, only if the union of the transposition of the adjacency matrix and the adjacency matrix is taken as the adjacency matrix, all the elements in the reachable matrix are 1.

5、Which of the following statements are true?
A、If a connected graph has r vertices, the rank of its complete correlation matrix is r-1.
B、The sum of the elements of each row of the completely related matrix corresponds to the degree of the vertex.
C、The elements in a row of the complete incidence matrix are all 0, and the corresponding vertices are isolated points.
D、The two columns corresponding to two parallel sides in the complete incidence matrix are the same.

6、Which of the following statements are true?
A、The diagonals of adjacency matrix are all zero only if the graph has no rings.
B、The adjacency matrix of a digraph is related to the order of the elements in its vertex set.
C、In the adjacency matrix of a digraph, a digraph must be constructed according to the n-matrix of given elements 0 and 1.
D、Given an adjacency matrix, a graph may not be constructed.

7、In adjacency matrix, exchange rows must exchange columns . Is that right?

13. Special Diagrams

Unit test of special drawing

1、A connected nontrivial undirected graph G has an Euler loop only if G is ()
A、No singularity node
B、There is only one singularity node.
C、There is only two singularity nodes.
D、There is only three singularity nodes.

2、Between a cut edge set and any spanning tree()
A、At least one common edge
B、Have no connection
C、The induced subgraph of cut edge set is a spanning tree
D、have a common side

3、If a tree has 7 leaves, 3 3 degree nodes and the rest are all 4 degree nodes, then the tree has () 4 degree nodes.
A、1
B、2
C、3
D、4

4、Which of the following is the prefix encoding
A、00,10,110,011
B、10, 000, 101, 01
C、111,000,110,11
D、010,110,01,101

5、Which of the following statements are true?
A、A graph with a circuit that passes through every edge of the graph once and only once is called an Euler graph.
B、An undirected graph has an Euler path only if the graph is connected and has two or zero odd degree vertices.
C、Undirected graphs have an Euler loop if and only if the graph is connected and all vertex degrees are even.
D、A directed graph has a one-way Euler path, only if the graph is connected, and except for two vertices, the degree of entry of each vertex is equal to the degree of exit.

6、Which of the following statements are true?
A、If G is a simple graph with n vertices, if the sum of degrees of each pair of vertices in G is greater than or equal to n-1, then there is a Hamiltonian path in G.
B、If G is a simple undirected graph, G is a Hamiltonian graph and only if its closure is a Hamiltonian graph.
C、Undirected graph G is bipartite only if the length of all circuits in G is even.
D、A connected undirected graph has at least one spanning tree.

7、If any two vertices of a acyclic graph are connected by a unique path, then this graph is a tree. Is that right?

Discrete Mathematics

Discrete Mathematics

1、Which of the following statements is not a proposition?
A、Do you like singing?
B、Beijing is the capital of the People's Republic of China.
C、Shaanxi Division Is a Factory.
D、If you're 7 plus 8and18,the trianglehas 4 sides.

2、P: PI'm sick,Q:When I go to school, "I don't go to school until I'm sick" ” can be symbolized as ( ).
A、
B、
C、
D、

3、The following proposition formula ( ) is not a restatement.
A、
B、
C、
D、

4、Which of the following proposition formulas is re-worded? ( )
A、
B、
C、
D、

5、The following formula is not a paradigm ( ).
A、
B、
C、
D、

6、The proposition formula is ( ) ?
A、Re-word
B、Contradiction
C、Non-permanently satisfied
D、Equivalent

7、The 3 number of propositional formulas with different true values with 3 proposition allots are ( ).
A、
B、
C、
D、

8、It M(x):x is a person, P(x):x making mistakes, and the proposition "no one who makes no mistake" is symbolized ( ) .
A、
B、
C、
D、

9、Which of the following are correct in predicate calculus?
A、
B、
C、
D、

10、Which of the following?
A、
B、
C、
D、

11、In the predicate formula , x is ().
A、It is both a free and a constrained variable
B、Free Variable
C、Constraint variables
D、Neither a free variable nor a constrained variable

12、Set all domain D is a set of positive integers, determining that the following proposition is true ( ) .
A、
B、
C、
D、

13、Predicate P(x):x is odd,Q(x):x is even, predicate formula is true in which individual domain? ( )
A、Natural number
B、Real
C、Plura
D、Rational numbers

14、What is the denial of Yongzheng( )?
A、Yongzheng
B、Permanent fake
C、Satisfied
D、Not sure

15、Formulas can be simplified to ( )
A、
B、
C、
D、

16、The domain of the medium word "x" is ( ).
A、
B、
C、
D、Not sure

17、R(x): x is a real number,Q(x): x is a rational number. Then the proposition "Not every real number is a rational number" ” is symbolized as ().
A、
B、
C、
D、

18、Given the predicate formula, the following formula is not its forearm paradigm ( ).
A、
B、
C、
D、

19、The following ( ) is a true proposition
A、
B、
C、
D、

20、Which of the following propositions is false,set A = { x,x is an integer and } ? ( )
A、
B、
C、
D、{ x|x is an integer and |x| <4}

21、set ,then B-A is ( )?
A、{ Φ，{ Φ}}
B、{ { Φ}}
C、{ Φ}
D、Φ

22、The following image describes a partial sequence set with a subset of the upper bound of (b, e, f) is ( )?
A、a,b
B、b,c
C、b
D、a,b,c

23、Both set and are dual-shot functions on X, then is ( ) .
A、
B、
C、
D、

24、The A={ a,{ a}} following proposition is wrong ( )
A、{ a}?P(A)
B、{ a}∈P(A)
C、{ { a}}∈P(A)
D、{ { a}}?P(A)

25、Write the correct symbol between 0（ ）Φ
A、?
B、=
C、?
D、∈

26、If the cardinality of set S is | S|=5, then the cardinality of power set S is |P(S) | = ( )
A、32
B、5
C、10
D、25

27、Set P={ x|(x+1)2≤4 and x∈R},Q={ x|5≤x2+16且x∈R},then which of the following propositions is correct ( )
A、
B、
C、
D、

28、If A-B=Ф, which of thefollowing conclusions is not possible? ( )
A、
B、
C、
D、

29、To judge which of the following propositions is true?
A、
B、An empty set is a true subset of any collection
C、An empty set is only a subset of a non-empty collection
D、If an element of A belongs to B,then A-B

30、Which of the following propositions is correct? ( )
A、{ Φ}≠Φ
B、Φ∈{ { Φ}}
C、All empty sets are not equal
D、If A is a non-empty set, then is established.

31、Which of the following propositions is correct? ( )
A、
B、
C、P(A∩B) ≠ P(A)∩P(B)
D、If A is non-empty set,then A≠ A ∪ A

32、A, B, C are three sets, which of the following reasoning is correct?
A、
B、
C、
D、None of the above inferences are correct.

33、Set S = { 1,2,3,4}, A on the relationship R = { <1,2>,<2,1>,<2,3>,<3,4>},then ( )
A、｛〈1,1〉，〈1,3〉，〈2,2〉，〈2,4〉｝
B、｛〈1,2〉，〈2,1〉，〈2,3〉，〈3,4〉｝
C、｛〈2,1〉，〈1,2〉，〈3,2〉，〈4,3〉｝
D、｛〈1,2〉，〈2,3〉，〈3,4〉，〈2,4〉｝

34、The relationship on the collection ,then the nature of R is ( )
A、Passed, symmetrical
B、Reflexive
C、Symmetrical
D、Passed

35、Set X={ a，b，c，d}，Y={ 1，2，3}，f={ <a，1>，<b，2>，<c，3>}，thefollowing proposition ( ) is true.
A、f is a binary relationship from X to Y, but not a function from X to Y;
B、f is a function from X to Y, but it is not a full shot, nor is it a single shot;
C、f is a full shot from X to Y, but not a single shot;
D、f is a double shot from X to Y.

36、Let <A, ≤> be a partial order set,,if is true,then y is ( )
A、The upper bound of the B
B、The lower bound of the B
C、The supremum bound of the B
D、The infimum bound of the B

37、An algebraic system with the following definition <G,*>, ( ) does not form a group
A、G=Q(Rational Number Set), * is a common multiplication
B、G={ 1,10},* is the mode 11 multiplication
C、G={ 1,3,4,5,9},* is the mode 11 multiplication
D、G=Q(Rational Number Set), * is a common addition

38、On the natural number set N, the following ( ) operations (for any natural number a,b) are binding.
A、a*b=max(a,b)
B、a*b=a-b
C、a*b=a+5b
D、a*b=|a-b|

39、For the natural number collection N,which operation is not binding, the operation is defined as any natural number a, b? ( )
A、a*b=a+2b
B、a*b=min(a,b)
C、a*b=a+b+3
D、a*b=b+a

40、Any half-group with multiple idems, it ( ).
A、Cannot form a group
B、Not necessarily a group.
C、Cannot form an exchange group
D、can form an exchange group.

41、Q is a rational set,and the operation defined * on Q is a*b=a +b-ab, then the unit-element of <Q,*> is ( )?
A、0
B、a
C、b
D、1

42、If A={ 3,6,9}, binary operation * on A is defined as: A *b=min{ A, b}, then in the unique point <A,*>, zero element is ( )?
A、3
B、6
C、9
D、None

43、Any subgroup of a 6th-order finite group must not be ( ) .
A、4 order
B、2 order
C、3 order
D、6 order

44、Given the following sequence, ( ) can constitute a sequence of nodes for a simple undirectiond graph.
A、（1，1，2，2，2）
B、（1，1，2，2，3）
C、（0，1，3，3，3）
D、（1，3，4，4，5）

45、Set the directionless graph G=<V,E>,|E|=12.There are known to be six 3-degree vertices, and the other vertices are all less than 3 degrees. Ask G at least ( ) vertices?
A、9
B、12
C、6
D、18

46、Set V={ a,b,c,d,e,f}，E={ <a,b>,<b,c>,<c,a>,<a,d>,<d,e>,<f,e>}，then directed graph G=<V,E> is ( )
A、Weakly connected
B、Strongly connected
C、One-sided
D、Unconnected

47、Here must be an even number ( ) in any graph.
A、Node with even degrees
B、The node of the entry degree is odd.
C、Nodes with odd degrees
D、The node of the outing is an odd number.

48、Setting G is a simple, directional graph that can reach the matrix P(G) to carve the following ( ) relationships.
A、Points and points
B、Points and edges
C、Edges and points
D、Edges and Edges

49、If a tree has two 2-degree nodes, one 3-degree node and three 4-degree nodes, then the number of 1-degree nodes is ( )
A、9
B、5
C、7
D、8

50、G is a tree, then G's spanning tree has ( ) tree.
A、1
B、0
C、2
D、I'm not sure

51、Set G is a tree, n, m represents the number of vertexs and the number of edges, respectively ( ).
A、n=m+1
B、n=m
C、m=n+1
D、I'm not sure

52、If the directionless figure G has 16 edges and the degree of each vertex is 2, the figure G has ( ) vertices.
A、16
B、10
C、4
D、8

53、If the directionless figure G has 18 edges and the degree of each vertex is 3, the figure G has ( ) vertices.
A、12
B、10
C、4
D、8

54、In a connectivity diagram with n vertices, the number of edges is ( ).
A、At least n-1.
B、Up to n-1
C、Up to n bars
D、At least n

55、A tree has 2 2-degree vertices, 1 3-degree vertices, and 3 4-degree vertices, and its 1-degree vertex is ( )
A、9
B、5
C、7
D、8

56、Which of the following diagrams is not necessarily a tree ( ) .
A、A graph of pathways between each pair of vertices
B、Connectivity diagram without simple loops
C、Connecting graph with n vertices n-1 edges
D、A connected but unconnected diagram with a cut-edge

57、Let's say tha

学习通Discrete Mathematics

学习通是中国领先的在线教育平台之一，致力于为学生和教师提供高质量的在线课程和学习资源。其中，Discrete Mathematics（离散数学）是学习通上的一门非常重要的课程之一。本文将介绍Discrete Mathematics的相关内容。

什么是Discrete Mathematics？

Discrete Mathematics是一门研究离散对象和离散结构的数学学科，与连续数学相对应。它涉及了诸如图论、逻辑、集合论、代数、组合数论等领域，是计算机科学、信息技术、工程学、数学和其他相关学科的基础。

为什么要学习Discrete Mathematics？

Discrete Mathematics作为计算机科学和信息技术的基础课程之一，它的重要性不言而喻。学习Discrete Mathematics可以帮助我们更好地理解计算机科学和信息技术的基本概念，如数据结构、算法、编程语言等。同时，它也是解决实际问题的有效工具，比如在网络安全、数据加密、人工智能等领域。

Discrete Mathematics的主要内容

Discrete Mathematics包括以下主要内容：

逻辑与证明

逻辑与证明是Discrete Mathematics中的一个重要分支。它主要研究命题、谓词、命题逻辑、谓词逻辑等基本概念，以及如何使用证明方法建立命题的真假。逻辑与证明是计算机科学中的基础，它可以帮助我们更好地理解程序的正确性、复杂性分析等概念。

集合论

集合论是Discrete Mathematics中的另一个重要分支。它主要研究集合、子集、运算等基本概念，以及如何使用这些概念描述和解决实际问题。

图论

图论是Discrete Mathematics中的一个重要分支。它主要研究图、网络、图结构等基本概念，以及如何使用这些概念分析和解决实际问题。图论在计算机科学、信息技术、网络安全等领域有广泛的应用。

组合数学

组合数学是Discrete Mathematics中的另一个重要分支。它主要研究如何计数、排列、组合等问题，以及如何使用这些方法解决实际问题。组合数学在计算机科学、信息技术、通信、加密等领域都有广泛的应用。

Discrete Mathematics的学习方法

在学习Discrete Mathematics时，我们可以采用以下方法：

多做练习

Discrete Mathematics需要大量的练习来掌握，因为它的概念和方法都比较抽象。我们可以通过做一些典型题目来熟悉和掌握这些概念和方法，同时也可以提升自己的逻辑思维能力。

参考教材和课程

Discrete Mathematics的教材和课程很多，我们可以选择一些质量较高的教材和课程来参考。比如，计算机科学经典教材《算法导论》中就有关于Discrete Mathematics的相关内容。

交流和讨论

在学习Discrete Mathematics时，我们可以和同学、老师或者其他人交流和讨论。这样不仅可以更好地理解和掌握知识，还可以发现自己的不足之处，以便及时纠正。

总结

Discrete Mathematics是一门非常重要的学科，它是计算机科学、信息技术、工程学、数学等学科的基础。学习Discrete Mathematics可以帮助我们更好地理解和掌握这些学科的基本概念和方法，同时也可以帮助我们解决实际问题。