令S为一组元素。 S上最大和最小等价关系中的有序对的数目为:
(A) n和n
(B) n 2和n
(C) n 2和0
(D) n和1答案: (B)
解释:
Consider an example set, S = (1,2,3)
Equivalence property follows, reflexive, symmetric
and transitive
Largest ordered set are s x s =
{ (1,1) (1,2) (1,3) (2,1) (2,2) (2,3) (3,1) (3,2)
(3,3) } which are 9 which equal to 3^2 = n^2
Smallest ordered set are { (1,1) (2,2) ( 3,3)}
which are 3 and equals to n. number of elements.
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