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 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)dot Show that varphi is the identity element for * on P\ (X) .

Define a binary operation on a set.

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

Define a commutative binary operation on a set.

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

Let A be a set having more than one element. Let '*' be a binary operation on A defined by a*b=sqrt(a^2 + b^2) for all a , b , in A . Is '*' commutative or associative on A?