Find whether the operation * is a binary operation or not on the given set : `a**b=a^b` on N

Find whether the operation * is a binary operation or not on the given set : a**b=|a-b| on Z.

Find whether the operation * is a binary operation or not on the given set : a**b=sqrt(a^2+b^2) on W

Find whether the operation * is a binary operation or not on the given set : a**b=(a-1)/(b+1) on Q

Is multiplication a binary operation on the set {0} ?

Give an example to show that suntraction is not a binary operation on the set of natural numbers.

Let ** be a binary operatiion defined by a**b=3a+4b-2 .Find 4**5 ?

Does the operation * defined below on the given set represent a binary operation? : a**b=ab on Z^+

Does the operation * defined below on the given set represent a binary operation? : a**b=a-b on Z^+

Let * be a binary operation defined by a*b = 3a+4b-2 find 4*5

In the set of integers Z, exmine whether the following relations are equivalence relations or not : R={(a,b) : a,b in Z and a