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Let P be the set of all subsets of a giv...

Let P be the set of all subsets of a given set X. Show that `uu: P xx P->P`given by `(A , B) ->Auu B`and ` nn: PxxP ->P`given by `(A , B)->AnnB`are binary operations on the set P.

Text Solution

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P= { all the subsets}
`X= {a,b}`
`P= { phi, {a}, {b}, {a,b}}`
`uu (A,B)= A uu B`
`A = phi , B= {a}`
`uu (A,B) -> A uu B -> {a}`
`nn (A,B) -> A nn B`
`n(A,B) -> A nn B-> { phi}-> phi`
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