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Let X be a nonempty set and *be a binary...

Let X be a nonempty set and *be a binary operation on `P(X),` the power set of `X,` defined by `A * B=A nn B` for all `A, B in P(X).` (

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`X={1, 2, 3}`
`P(x)={phi, {1}, {2}, {3}, {1, 2}, {2, 3}, {1, 3}, {1, 2, 3}}`
`A * X=A cap X= A`
`X * A= X cap A=A`
Let `e` be the identity of * then `a*e=e*a=a`
So `A *X=A=X*A` for all `A in P(X)`
`X` is the identity element
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