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

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

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

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.

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:

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

a ** b = a^(b) AA a, b in Z . Show that * is not a binary operation on Z by giving a counter example.

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.

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.

Determine whether or not the definition of * On Z^(+) ,define * 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.