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Let S be a non-empty set and P(s) be the...

Let S be a non-empty set and `P(s)` be the power set of set S. Find the identity element for all union `()` as a binary operation on `P(S)dot`

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Let S be a non-empty set and `P(s)` be the power set of set S.
Then we see that
`A cup phi=A=phi cup A` for every subset A of set S.
`A cup phi=A=phi cup A` for all `A in P(S)`
Therefore,`phi` is the identity element for all union `(cup)` on P(S).
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