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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 subjects of `X` . Define a relation in `P\ (X)` as follows: For subjects `A ,\ B` in `P\ (X),\ \ A\ R\ B` if `AsubB` . Is `R` an equivalence relation on `P\ (X)` ? Justify your answer.

Text Solution

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`P(X) = {`All subsets`}`
`R = {(A,B): A sub B}`
As `A sub A`
`:. (A,A) in R`
`:. R` is reflexive.
Let `(A,B) in R`
Then, `A sub B`
...
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