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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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We observe 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) `
` phi `is the identity element for union` (U) `on `P(S).`
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RD SHARMA-BINARY OPERATIONS-Solved Examples And Exercises
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  17. Determine whether O on Z defined by a\ O\ b=a^b for all a ,\ b in ...

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  18. Determine whether * on N defined by a*b=a+b-2 for all a ,\ b in N ...

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