Determine whether the following is a binary operation or not?Justify `a**b=2^(ab)`defined on Z

Determine which of the following binary operation on the set R are associative and which are communtative. a ** b=1

Check whether the following binary operation on the set R are associative and commutative. a ** b=((a+b))/2AAa,b in R

State whether the following statements are true or false. Justify For an arbitary binary operation ** on N, a**a=a AA a in N

Determine whether each of the following relations is reflexive, symmetric and transitive. Relation R in the set Z of all integers defined as R = {(x,y) :x-y is an integer}

State whether the following statements are true or false. Justify If ** is a commutative binary operation on N, then a**(b**c)=(c**b)**a

ast ' is a binary operation on R defined as aastb=2ab Find the inverse element, if exists

Determine whether or not each of the definitions of ** given below gives a binary operation. In the event that ** is not a binary operation, give justification for this on Z^+ , define ** by a**b=ab

Determine whether or not each of the definitions of ** given below gives a binary operation. In the event that ** is not a binary operation, give justification for this on R , define ** by a**b=ab^2

Determine whether or not each of the definitions of ** given below gives a binary operation. In the event that ** is not a binary operation, give justification for this on Z^+ , define ** by a**b=a-b

Determine whether or not each of the definitions of ** given below gives a binary operation. In the event that ** is not a binary operation, give justification for this on Z^+ , define ** by a**b=|a-b|