Given a non-empty set X, let `* : P(X)xxP(X)rarrP(X)`, be defined as `A * B = (A – B) cup (B – A), forall A, B in P(X)`.Show that the empty set `phi` is the identity for the operation * and all the elements A of P(X) are invertible with `A^–1 = A`.

Given a non - empty set, X , consider the binary operation ** : P(X) xxP(X) rarr P(X) given by A **B = Acap B , AAA,B in P(X) , where P(X) is the power set X. Show that X is the identity element for this operation and X is the only invertible element in P(X) with respect to the operation ** .

Let X be a non-empty set. P(X) be its power set. Let * be an operation defined on elements of P(X) by A * B = A cup B forall AB in P(X) . Then prove that * is a binary operation.

Let X be a non-empty set. P(X) be its power set. Let * be an operation defined on elements of P(X) by A * B = A cup B forall AB in P(X) . Then Is * Associative ?

Let X be a non-empty set. P(X) be its power set. Let * be an operation defined on elements of P(X) by A * B = A cup B forall AB in P(X) . Then Find the identity element in P(X) w.r.t. *

Define a binary operation * on the set {0, 1, 2, 3, 4, 5} as a*b = { a + b , if a+ b < 6 a+b-6 , if a+bge6 . Show that zero is the identity for this operation and each element 'a' of the set is invertible with (6-a) being the inverse of a.

Let X be a non-empty set. P(X) be its power set. Let * be an operation defined on elements of P(X) by A * B = A cup B forall AB in P(X) . Then Is *Commutative ?

Define a binary operation * on the set {0,1,2,3,4,5} as a*b = {:{(a+b, if a +b < 6),(a+b-6, if a +bge6):} Show that zero is the identity for this operation and each element ane0 of the set is invertible with 6 - a being the inverse of a.

Let X be a non-empty set. P(X) be its power set. Let * be an operation defined on elements of P(X) by A * B = A cup B forall AB in P(X) . Then V If 0 is another binary operation defined on P(X) as AOB=A cap B then verify that 0 distributes itself over*.

Let A be a non-empty set and '*' be a binary operation on P(A), the power set of A, defind by X*Y = X uu Y for all X, Y in P(A) Show that phi in P (A) is only invertible element w.r.t '*'

Let '*' be the operation defined on the set R - (0) by the rule a * b = (ab)/(5) for all a, b in R - (0). Write the identity element for this operation.