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 nn B AA A, B in P (X)`. Then: Is '*' commutative ?

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 nn B AA A, B 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 nn B AA A, B in P (X) . Then: Prove that '*' is a binary operation on P (X)

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 nn B AA A, B in P (X) . Then: Find the identity element in P (X) w.r.t. 'X'.

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 ?

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 and P(X) be its power set . Let * be an operation defined on elements of P(X), by: A*B = A nn B AA A, B in P(X) Then, If 'o' as AoB = A uuB , then verify that 'o' distributes itself over. *

Let 'X' be a non-empty set and P(X) be its power set . Let * be an operation defined on elements of P(X), by: A*B = A nn B AA A, B in P(X) Then, Find all invertible elements of P(X).

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 V If 0 is another binary operation defined on P(X) as AOB=A cap B then verify that 0 distributes itself over*.

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. *