教育
-Discrete Mathematics-章节资料考试资料-University of Science and Technology Beijing【】
Chapter 1 unit tests
1、【单选题】Which is a proposition in the following statements?
A、Please don’t copy!
B、The sun is a planet.
C、Can I smoke here?
D、x – y = 3
参考资料【 】
2、【单选题】Which is an atomic statement in the following statements?
A、Zhang San and LiSi are friends.
B、If it rains tomorrow, I won’t go to the park.
C、There is no savior or god.
D、Xiao Ming is either in class or running on the playground.
参考资料【 】
3、【单选题】Suppose P: I’m ChineseQ: I come from BeijingUnless I am from Beijing, I am not Chinese is the result of the symbolic statement:
A、
B、
C、
D、
参考资料【 】
4、【单选题】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.
参考资料【 】
5、【单选题】Which is the simplified form of the following combination formulas:?
A、
B、
C、
D、
参考资料【 】
6、【单选题】According to the implication law, which one is equivalented in the following formulas？
A、
B、
C、
D、
参考资料【 】
7、【单选题】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
参考资料【 】
8、【单选题】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
参考资料【 】
9、【单选题】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
参考资料【 】
10、【单选题】What is the dual of?
A、
B、
C、
D、
参考资料【 】
11、【单选题】What is the type of?
A、tautologies
B、contradiction
C、Nontautological satisfiable formula
D、Unable to determine
参考资料【 】
12、【单选题】Which one is conjunctive and disjunctive paradigms?
A、
B、
C、
D、
参考资料【 】
13、【多选题】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.
参考资料【 】
14、【多选题】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?
参考资料【 】
Chapter 2 unit tests
1、【单选题】Which one is not a predicate formula?
A、
B、
C、
D、
参考资料【 】
2、【单选题】In the formula，the free variable is()
A、第一个x
B、第二个x
C、y
D、z
参考资料【 】
3、【单选题】Which one is wrong?
A、
B、
C、
D、
参考资料【 】
4、【单选题】Which one is wrong?
A、
B、
C、
D、
参考资料【 】
5、【单选题】Which one is wrong?
A、
B、
C、
D、
参考资料【 】
6、【单选题】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、
参考资料【 】
7、【单选题】Which one is the prenex normal form?
A、
B、
C、
D、
参考资料【 】
8、【多选题】Suppose the individual domain is a set of integers. Which has a true value of 0 in the following formulas?
A、
B、
C、
D、
参考资料【 】
9、【多选题】Which is correct in the following formula?
A、
B、
C、
D、
参考资料【 】
10、【多选题】Which is not the Negation of formula?
A、
B、
C、
D、
参考资料【 】
11、【判断题】The type of well-formed formulais Tautology
A、正确
B、错误
参考资料【 】
12、【判断题】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.
A、正确
B、错误
参考资料【 】
13、【判断题】The type of formulais Tautology
A、正确
B、错误
参考资料【 】
14、【判断题】Let the individual domain be A = {a, b}, The formulaafter eliminating the quantifier should be.
A、正确
B、错误
参考资料【 】
15、【判断题】Determine whether this formula is correct:
A、正确
B、错误
参考资料【 】
Chapter 3 unit tests
1、【单选题】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}
参考资料【 】
2、【单选题】What’s wrong?
A、
B、
C、
D、
参考资料【 】
3、【单选题】Which of the following is wrong ?
A、
B、
C、
D、
参考资料【 】
4、【单选题】On [1, 100], how many integers can’t be divided by 3 and 5 or 7?
A、45
B、27
C、33
D、62
参考资料【 】
5、【单选题】A. B and C are arbitrary sets. What’s right?
A、
B、
C、
D、if,then
参考资料【 】
6、【单选题】A. B is any set. What’s the error?
A、
B、
C、
D、
参考资料【 】
7、【单选题】A. B and C are arbitrary sets. What’s right?
A、
B、
C、
D、
参考资料【 】
8、【多选题】Known ,what the method of solving the order of the value of and ?
A、
B、
C、
D、
参考资料【 】
9、【多选题】Due to ,what can be deduced?
A、
B、
C、
D、
参考资料【 】
10、【多选题】What laws are used in the following reasoning?
A、Law of identity
B、Law of distribution
C、Law of zeros
D、Commutative law
参考资料【 】
11、【判断题】
A、正确
B、错误
参考资料【 】
12、【判断题】Suppose a, B and C are any set,
A、正确
B、错误
参考资料【 】
13、【判断题】
A、正确
B、错误
参考资料【 】
14、【判断题】
A、正确
B、错误
参考资料【 】
15、【判断题】
A、正确
B、错误
参考资料【 】
16、【判断题】Suppose a, B and C are non null sets,ifand,then.
A、正确
B、错误
参考资料【 】
unit test of binary relation
1、【单选题】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
参考资料【 】
2、【单选题】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
参考资料【 】
3、【单选题】A. B, C and D are arbitrary sets. What’s right?
A、
B、
C、
D、
参考资料【 】
4、【单选题】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
参考资料【 】
5、【多选题】R is a binary relationship, and , which of the following is not necessarily transitive?
A、
B、
C、
D、
参考资料【 】
6、【判断题】There are 255 binary relations on a = {1, 2, 3, 4, 5}
A、正确
B、错误
参考资料【 】
7、【判断题】A = {a, b}, R is the relationship on A, r = { a, a , b, b }, then R is not transitive.
A、正确
B、错误
参考资料【 】
functional unit test
1、【单选题】Considering the function on the real number set, the analytic expression of is
A、
B、
C、
D、
参考资料【 】
2、【单选题】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 }
参考资料【 】
3、【单选题】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
参考资料【 】
4、【单选题】Suppose A and B are finite sets,|A|=n，|B|=m，and n,m0，then
A、
B、
C、
D、
参考资料【 】
5、【多选题】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.
参考资料【 】
6、【判断题】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.
A、正确
B、错误
参考资料【 】
7、【判断题】The number of elements of set a is n, and the number of elements of set B is m. There are mn kinds of different bijections from set a to set B.
A、正确
B、错误
参考资料【 】
unit test of algebra system
1、【单选题】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
参考资料【 】
2、【单选题】Which of the following is not a binary operation on the integer set Z?
A、division
B、addition
C、subtraction
D、multiplication
参考资料【 】
3、【单选题】On the natural number set N, which of the following operations can be combined?
A、ab=max{a,b}
B、ab=a-b
C、ab=a+2b
D、ab=|a-b|
参考资料【 】
4、【单选题】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
参考资料【 】
5、【单选题】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
参考资料【 】
6、【单选题】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
参考资料【 】
7、【单选题】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
参考资料【 】
8、【单选题】Q is the rational number set N, and the definition operation * on Q is ab= a + b – ab, then the unit elements of Q, * is
A、0
B、a
C、b
D、1
参考资料【 】
9、【单选题】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)=xx
参考资料【 】
10、【单选题】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>
参考资料【 】
11、【单选题】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}
参考资料【 】
12、【多选题】On the natural number set n, which of the following operations are commutative?
A、ab=max{a,b}
B、ab=|a-b|
C、ab=a-b
D、ab=a+2b
参考资料【 】
13、【多选题】Which of the following is a binary operation on n?
A、addition
B、multiplication
C、subtraction
D、division
参考资料【 】
14、【多选题】Which of the following is not a binary operation on n?
A、subtraction
B、division
C、addition
D、multiplication
参考资料【 】
15、【多选题】V=R*,×, which of the following functions are homomorphisms of V to v?
A、f(x)=xx
B、f(x)=1/x
C、f(x)=2x
D、f(x)= -x
参考资料【 】
16、【判断题】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.
A、正确
B、错误
参考资料【 】
17、【判断题】In an operation table, if the elements of an element’s row and column are the element itself, then the element is zero.
A、正确
B、错误
参考资料【 】
18、【判断题】If the elements of the operation table are symmetrically distributed about the main diagonal, the operation can be combined.
A、正确
B、错误
参考资料【 】
preliminary unit test of group theory
1、【单选题】Any subgroup of a finite group of order 6 must not be()
A、Rank 4
B、Rank 2
C、Rank 3
D、Rank 6
参考资料【 】
2、【单选题】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
参考资料【 】
3、【单选题】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
参考资料【 】
4、【单选题】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
参考资料【 】
5、【单选题】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
参考资料【 】
6、【单选题】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
参考资料【 】
7、【单选题】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
参考资料【 】
8、【单选题】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
参考资料【 】
9、【单选题】The subgroups of group Z4, ⊕ is
A、<{0,2},⊕>
B、<{0,1},⊕>
C、<{0,3},⊕>
D、<{0,1,3},⊕>
参考资料【 】
10、【单选题】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
参考资料【 】
11、【单选题】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
参考资料【 】
12、【单选题】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
参考资料【 】
13、【多选题】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
参考资料【 】
14、【多选题】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
参考资料【 】
15、【多选题】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>
参考资料【 】
16、【多选题】If G,* is a group, then * is()
A、Satisfied combination law
B、Have Unit element
C、Every unit has inverse element
D、Exchangeable
参考资料【 】
17、【判断题】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.
A、正确
B、错误
参考资料【 】
18、【判断题】Groups of prime order must be cyclic groups.
A、正确
B、错误
参考资料【 】
19、【判断题】The number of elements of order 2 in even order groups must be odd
A、正确
B、错误
参考资料【 】
20、【判断题】The number of elements with order greater than 2 in a finite group must be even.
A、正确
B、错误
参考资料【 】
21、【判断题】There is no zero element in a group with at least two elements.
A、正确
B、错误
参考资料【 】
22、【判断题】a is the generator of a group〈G，〉, then the inverse of a is also the generator of a group〈G，*〉.
A、正确
B、错误
参考资料【 】
23、【判断题】There must be an element of order 2 in an even order group.
A、正确
B、错误
参考资料【 】
24、【判断题】Group G has no idempotent except unit element.
A、正确
B、错误
参考资料【 】
basic concept unit test of Graphs
1、【单选题】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
参考资料【 】
2、【单选题】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
参考资料【 】
3、【单选题】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)
参考资料【 】
4、【单选题】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
参考资料【 】
5、【多选题】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.
参考资料【 】
6、【判断题】In a graph, there are both directed and undirected edges. Such a graph is called a mixed graph. Is that right?
A、正确
B、错误
参考资料【 】
7、【判断题】A simple graph in which all vertices have the same degree is called a regular graph. Is that right?
A、正确
B、错误
参考资料【 】