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Given a non-empty set X , consider P\ (X...

Given a non-empty set `X` , consider `P\ (X)` which is the set of all subsets of `X` . Define a relation in `P\ (X)` as follows: For subsets `A ,\ B` in `P\ (X),\ \ A\ R\ B` if `AsubB` . Is `R` an equivalence relation on `P\ (X)` ? Justify your answer.

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`P(X)=\{A: A` is a subset of X`\}`

(i) Since `A C A \forall \in P(X)`

`\therefore ARA \forall A \in P(X)`

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