1.

Let P be a set of all subset of set X. Prove that the functions defined by cup : P xx P to P, (A,B) to A cupB and cap : PxxP to P, (A,B) to A cap Bare binary on P.

Answer»

Solution :`:'` Union operation `CUP` relates every PAIR (A,B) of `P XX P` to unique element of `A cup B`.
`:.` It is a binary operation.
`:.` Intersection operation `cap` relates every pair (A,B) of `P xx P` to unique element of `A cap B`
`:.` It is a binary operations.
HENCE PROVED.


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