Discrete Mathematics(University of Science and Technology Beijing) 中国大学MOOC答案2024版100分完整版

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}