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) .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 N. is * associative or commutative on N?

Let t be a binary operation on Q_(0)( set of non- zero rational numbers) defined by a*b=(3ab)/(5) for all a,b in Q_(0) Find the identity element.

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

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 Q_0 (set of all non-zero rational numbers) defined by a*b=(a b)/4 for all a , b in Q_0dot Then, find the identity element in Q_0 inverse of an element in Q_0dot

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