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 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). (

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 * be a binary operation on N, the set of natural numbers, defined by a*b= a^b for all a , b in Ndot Is '*' commutative on N ?

Let X be any non-empty set containing n elements, then the number of relations on X is

Let * be a binary operation on set of integers I, defined by a*b=2a+b-3. Find the value of 3*4.

Let A=NxxN , and let * be a binary operation on A defined by (a ,\ b)*(c ,\ d)=(a d+b c ,\ b d) for all (a ,\ b),\ (c ,\ d) in NxxNdot Show that A has no identity element.

Let * be a binary operation on Q_0 (set of non-zero rational numbers) defined by a*b=(3a b)/5 for all a , b in Q_0dot Find the identity element.

Let * be a binary operation on Q_0 (set of non-zero rational numbers) defined by a*b= (3a b)/5 for all a ,\ b in Q_0 . Show that * is commutative as well as associative. Also, find the identity element, if it exists.

Let * be a binary operation on N, the set of natural numbers, defined by a*b= a^b for all a , b in Ndot Is '*' associative or commutative on N ?

Let *, be a binary operation on N, the set of natural numbers defined by a*b = a^b , for all a,b in N . is * associative or commutative on N?