中国大学mooc慕课 Discrete Mathematics(University of Science and Technology Beijing) 答案满分完整版章节测试

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1. Propositional logic of mathematical logic Chapter 1 unit tests

1、 Which is a proposition in the following statements?

答案: The sun is a planet.

2、 Which is an atomic statement in the following statements?

答案: Zhang San and LiSi are friends.

3、 Suppose P: I’m ChineseQ: I come from Beijing”Unless I am from Beijing, I am not Chinese” is the result of the symbolic statement:

答案:

4、 Which is a false statement in the following statements?

答案: 2 is a prime number only if USTB is not in Beijing. 

5、 Which is the simplified form of the following combination formulas:?

答案:

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

答案:

7、 German Nazi leader goebbels once said that a lie repeated three times becomes a truth.Which law does this violate?

答案: Idempotent law

8、 “Stinky tofu stinks and smells good” is a false statement.Which law does this use?

答案: Law of contradiction

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?

答案: Disjunctive syllogism

10、 What is the dual of?

答案:

11、 What is the type of?

答案: Nontautological satisfiable formula

12、 Which one is conjunctive and disjunctive paradigms?

答案:

13、 Which are propositions in the following statements?(multiple choices)

答案: The shot is not a ball. ;
If he doesn’t play, we’ll lose.;
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

答案: I have classes every day. ;
Are there people on Mars?

15、 Which is a false statement in the following statements?

答案: 2 is a prime number only if USTB is not in Beijing. 

2. Predicate logic of mathematical logic Chapter 2 unit tests

1、 Which one is not a predicate formula?

答案:

2、 In the formula，the free variable is()

答案: y

3、 Which one is wrong?

答案:

4、 Which one is wrong?

答案:

5、 Which one is wrong?

答案:

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?

答案:

7、 Which one is the prenex normal form?

答案:

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

答案: ;
;

9、 Which is correct in the following formula?

答案: ;

10、 Which is not the Negation of formula?

答案: ;
;

11、 The type of well-formed formulais Tautology

答案: 错误

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.

答案: 正确

13、 The type of formulais Tautology 

答案: 正确

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

答案: 错误

15、 Determine whether this formula is correct:

答案: 错误

16、 Which is not the Negation of formula?

答案: ;
;

17、 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.

答案: 正确

18、 The type of formulais Tautology 

答案: 正确

3. Set of set theory Chapter 3 unit tests

1、 The cardinal numbers of which set is three?

答案:

2、 What’s wrong?

答案:

3、 Which of the following is wrong ?

答案:

4、 On [1, 100], how many integers can’t be divided by 3 and 5 or 7?

答案: 45

5、 A. B and C are arbitrary sets. What’s right?

答案:

6、 A. B is any set. What’s the error?

答案:

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

答案:

8、 Known ,what the method of solving the order of the value of  and ?

答案: ;

9、 Due to ,what can be deduced?

答案: ;

10、 What laws are used in the following reasoning? 

答案: Law of identity;
Law of distribution;
Law of zeros

11、

答案: 正确

12、 Suppose a, B and C are any set,

答案: 错误

13、

答案: 错误

14、

答案: 正确

15、

答案: 正确

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

答案: 错误

17、 A. B and C are arbitrary sets. What’s right?

答案:

18、 What laws are used in the following reasoning?

答案: Law of identity;
Law of distribution;
Law of zeros

19、 Suppose a, B and C are any set,

答案: 错误

4.Binary relation of set theory unit test of binary relation

1、 Which of the follwing has the Transitive relationship?

答案: The same year relationship of ancient imperial examination

2、 Which of the following is equivalent?

答案: Logical equivalence of propositional formula

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

答案:

4、 What’s right?

答案: The poset of a finite set must have the Maximal element

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

答案: ;
;

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

答案: 错误

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

答案: 错误

5. Functions of set theory functional unit test

1、 Considering the function on the real number set, the analytic expression of is

答案:

2、 Which of the following relationships can form a function?

答案: f={<x, y>| x,y∈N, and Y is the number of prime numbers less than x}

3、 Which of the following functions has an inverse function?

答案: f:N->N, f(x)=x

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

答案:

5、 Which of the following statement is correct ()

答案: A and B are two equal sets. The function from A to B is unijection only if it is a hyperjection.;
The inverse relations of functions are not always functions.;
Only bijective function is invertible, and its inverse function is bijective.

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.

答案: 正确

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.

答案: 错误

8、 Considering the function on the real number set, the analytic expression of is

答案:

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

答案:

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?

答案: f(x) = |x|

2、 Which of the following is not a binary operation on the integer set Z?

答案: division

3、 On the natural number set N, which of the following operations can be combined?

答案: a*b=max{a,b}

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