Let P(A) be the power set of a non-empty set A. Prove that union `(cup)` and intersection `(cap)` of two subsets X and Y of A are binary operations on P(A).

Let P(A) be the power set of a non-empty set A and a binary operation @ on P(A) is defined by X@Y=XcupY for all YinP(A). Prove that, the binary operation @ is commutative as well as associative on P(A). Find the identity element w.r.t. binary operation @ on P(A). Also prove that Phi inP(A) is the only invertible element in P(A).

Let P(A) b the power set of non-empty set A. A binary operation ** is defined on P(A) as X**Y=XcapY for all X,YinP(A) . Detemine the identity element In P(A). Prove that A is the only invertible element in P(A).

Let P(A) be the power set of a non-empty set A. A relation R on P(A) is defined as follows : R={(X,Y) : X sube Y} Example (i) reflexivity, (ii)symmetry and (iii) transitivity of R on P(A).

If A is a non empty set, prove that the operation union on P(A) is a binary operation.

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 A be any non-empty set.Then,prove that the identity function on set A is a bijection.

Let A be any non-empty set. Then, prove that the identity function on set A is a bijection.

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 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)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