In `(z, **)` where `**` is defined by `a ** b=a^b`, prove that `**` is not a binary operation on z.

On Z defined * by a ** b = a -b show that * is a binary operation of Z.

The operation ** is defined by a**b=a^(b) on the set Z={0,1,2,3,…} . Show that ** is not a binary operation.

The operation @ is defined by a@b=b^(a) on the set Z={0,1,2,3,…} . Prove that @ is not a binary opeartion on Z.

Show that * on Z^(+) defined by a*b=|a-b| is not binary operation

The operation ** defined by a**b = b^(a) on the set Z = {0,1,2,3,. . . } . Prove that ** is not a binary operation on Z.

The operation * defined a**b = a . Is * a binary operation on z.

Determine whether O on Z defined by a\ O\ b=a^b for all a ,\ b in Z define a binary operation on the given set or not:

On Z, the set of all integers,a binary operation * is defined by a*b=a+3b-4 Prove that * is neither commutative nor associative on Z.

Prove that the operation ** on ZZ defined by a**b=a|b| for all a,binZZ is a binary operation

Determine whether or not the definition of * On Z^(+) ,defined * by a*b=a-b gives a binary operation.In the event that * is not a binary operation give justification of this. Here,Z^(+) denotes the set of all non-negative integers.