課本上有一個題目
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 (課本上寫R bar 但是我打不
出
來）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.
課本的解答是直接用X={1,2,3}當例子去解，
錯誤的是可以直接舉出反例沒問題，但是正確的這樣做應該不算證明吧？
想問這題有沒有更精確的證明方式呢？
謝謝
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※ 編輯: amamoimi (180.217.5.40 臺灣), 11/04/2023 22:29:14