求解一道高级微观的题目

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Let 大于等于（类似于大于等于的符号） be a refexive and complete binary relation and let 大于 be its associated strict
preference (x 大于y if and only if x 大于等于 y and y 不大于等于 x). If 大于is transitive, can you conclude
that so is 大于等于?

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关键词：高级微观 Preference Associate Reference relation relation

reflexive打错了

没有人会么很着急额

I am not sure, but I think it is yes.
Let reflexive and complete be assumed.
When x大于等于y, it follows that (a) y不大于等于x or (b)y大于等于x.
When y大于等于z, it follows that (c) z不大于等于y or (d)z 大于等于y.
If 大于 is transitive, that means that x大于等于y and y不大于等于x combined with y大于等于z and z不大于等于y can lead to x大于等于z and z不大于等于x.
Then if x大于等于y and y大于等于z, from all conditions (a)(c), (a)(d), (b)(c), (b)(d), it can be shown that x大于等于z. That means 大于等于is transitive.

我也正在学习，分享一点自己的见解，期待高手解答。