Discrete Mathematics - 中国大学mooc

1. Propositional logic of mathematical logic

Chapter 1 unit tests

1、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

2、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.

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

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 formula is 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 of is 1.

13、The type of formula is Tautology

14、Let the individual domain be A = {a, b}, The formula after 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,if and ,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.