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Let x be a nonempty set and * be a binary operation on P(X) the power set of X defiend by A*B =A cap B for all A,B in P(x) ltrbgt (i)Find the identity element in P(x) (ii) show that X is the only inveritiableelement in P(x)

Answer»


Solution :(i) Since `A cap X=A forall A ub P(x)`
`therefore` X is the identity element
(ii) LET A be invertible in p(x) and let B its INVERSE
then `A cap B = X`
This is POSSIBLE only whne A=B =X
`therefore`X is the only inveritable element in P(x) and its inverse is X


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