作者amamoimi (佛仔)
看板Math
标题[离散] relation相关问题
时间Sat Nov 4 22:27:06 2023
课本上有一个题目
suppose that R is a relation on X that is symmetric and transitive but not reflx
ive. Suppose also that |X| >=2. Define the relation P (课本上写R bar 但是我打不
出
来）on X by =X× X-R. Which of the following must be true? for each false state
ent, provide a counterexample.
a. P is reflxive
b. P is symmetric
c. P is not antisymmetric.
d. P is transtive.
课本的解答是直接用X={1,2,3}当例子去解，
错误的是可以直接举出反例没问题，但是正确的这样做应该不算证明吧？
想问这题有没有更精确的证明方式呢？
谢谢
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※ 编辑: amamoimi (180.217.5.40 台湾), 11/04/2023 22:29:14