For the binary operation `**` defined below, determine whether `**` is commutative and associative : On N, define `a**b=2^(ab)`

For the binary operation ** defined below, determine whether ** is commutative and associative : On N, define a**b=a^b

For the binary operation ** defined below, determine whether ** is commutative and associative : On Q, define a**b=(ab)/2

For the binary operation ** defined below, determine whether ** is commutative and associative : On Z, define a**b=ab+1

Is the binary operation ** defined by Q by a**b=(a+b)/2 for all a,b in Q commutative and associative?

Define determinate growth.

Is the binary operation ** defined on the set of integer Z by the rule a**b=a-b+2 commutative ?

Is the binary operation ** defined on the set of rational numbers by the rule a**b=ab//4 associative ?

Let A=NxxN and let ** be a binary operation on A defined by (a,b)**(c,d)=(a+c,b+d) . Show that ** is commutative and associative.

Is the binary operation ** defined on Z (set of integers) by the rule a**b=a-b+ab for all a, bin Z commutative ?