Now, for example.
Third, judge the explanation questions (judge the following questions and explain the reasons. )
1. If the binary relation r = {< 1,1> , & lt22,2 & gt,< 1, 2>}, then
(1) R is reflexive; (2) R is a symmetric relation.
2. If R 1 and R2 are reflexive on a, then is it true to judge that "R-1,R 1∪R2, R 1∪R2 are reflexive"? And explain why.
3. Let R and S be symmetrical on set A, and judge whether R∩S is symmetrical and explain the reasons.
4. Let the sets A={ 1, 2,3,4} and B = {2,4,6,8} to determine whether the following relationship F constitutes the function F:, and explain the reasons.
( 1)f = { & lt； 1，4 & gt，& lt2，2，& gt，& lt4，6 >，& lt 1，8 & gt}; (2)f = { & lt； 1，6 & gt，& lt3，4 & gt，& lt2，2 & gt};
(3)f = { & lt； 1，8 & gt，& lt2，6 >，& lt3，4 & gt，& lt4，2，& gt}.
Fourth, the calculation problem
1. set, q:
( 1) (A？ b)？ ~ C； (2) (A？ B)- (B？ A)(3)P(A)-P(C)； (4) a? B.
2. Let the sets A = {{A, B}, C, D}, B={a, B, {c, d }} be combined.
( 1) B？ a； (2) a? b； (3)A-B； (4)B？ A.
3. Let a = {1, 2, 3, 4, 5} and r = {
4. Let A={ 1, 2, 3, 4, 5, 6, 7, 8}, R is the divisible relation on A, and B = {2, 4, 6}.
(1) Write the expression of relation r; (2) Draw a Haas diagram of the relation r;
(3) Find the largest element and the smallest element of set B. 。
Verb (abbreviation of verb) proves the problem
1. Try to prove the set equation: a? (B？ C)=(A？ b)？ (A？ c)。
2. For any three sets A, B and C, try to prove that if A B = A C, A, then B = C. 。
3. Let R be the symmetric relation and transitive relation on set A, and try to prove that if any A? A and b? First, production
1.( 1) Is there an error?
(2) The only mistake is
2. "r-11,R 1∪R2, r 1∪R2 are reflexive" are invalid, valid and valid respectively, and the reasons are explained according to the definition of reflexivity.
3. There is symmetry, which can be defined and explained according to the symmetry of binary relationship.
4. Only (3) constitutes a functional relationship.
Fourth,
Sorry, some topics are unclear, and the symbols are not typed ... For these topics, please refer to Discrete Mathematics (second edition) edited by Liu Yuzhen Liu Yongmei, Wuhan University Press.