On the set `W` of all non-negative integers `*` is defined by `a*b=a^b` . Prove that `*` is not a binary operation on `Wdot`

An operation * on z^(+) ( the set of all non-negative integers) is defined as a * b = |quad a -b|, AA q,b in z^(+) .Is * a binary operation on z^(+) ?

An operation ** on Z^(**) (the set of all non-negative integers) is defined as a**b = a-b, AA a, b epsilon Z^(+) . Is ** binary operation on Z^(+) ?

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.

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 Zdot

On the set Z of integers a binary operation * is defined by a*b=ab+1 for all a,b in Z Prove that * is not associative on Z

An operation ** on ZZ , the set of integers, is defined as, a**b=a-b+ab for all a,binZZ . Prove that ** is a binary operation on ZZ which is neither commutative nor associative.

On the set Q of all rational numbers if a binary operation * is defined by a*b=(ab)/(5), prove that * is associative on Q.

On the set Q of all rational numbers if a binary operation * is defined by a*b= (a b)/5 , prove that * is associative on Qdot

On the set Z of integers a binary operation * is defined by a*b= a b+1 for all a ,\ b in Z . Prove that * is not associative on Zdot