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Let A={a,b,{a,b}}, where P(A) is the pow...

Let A={a,b,{a,b}}, where P(A) is the power set of A, then P(A)=

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Statement-1 P(A)nnP(B)=P(AnnB) , where P(A) is power set of set A. Statement-2 P(A)uuP(B)=P(AuuB) .

Find the power set of the set {a,b,c}.

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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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) .

Let X be a non-empty set and let * be a binary operation on P(X) (the power set of set X) defined by A*B=AuuB for all A ,\ B in P(X) . Prove that * is both commutative and associative on P(X) . Find the identity element with respect to * on P(X) . Also, show that varphi in P(X) is the only invertible element of P(X)dot

Let S be a non-empty set and P(s) be the power set of set S. Find the identity element for all union U as a binary operation on P(S)dot

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Let X be a non-empty set and let * be a binary operation on P\ (X) (the power set of set X ) defined by A*B=(A-B)uu(B-A) for all A ,\ B in P(X)dot Show that varphi is the identity element for * on P\ (X) .

Let X be a non-empty set and let * be a binary operation on P\ (X) (the power set of set X ) defined by A*B=(A-B)uu(B-A) for all A ,\ B in P(X)dot Show that varphi is the identity element for * on P\ (X) .