'o' on N defined by a o b= a b + b a for all a, b∈N define a binary operation on the given set or not:

:' on Q defined by a*b=(a-1)/(b+1) for all a,b in Q define a binary operation on the given set or not:

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

Determine whether * on N defined by a*b=a+b-2 for all a,b in N 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:

Determine whether '+_(6)^(prime) on S={0,1,2,3,4,5} defined by a+6b={a+b,quad if quad a+b =6 define a binary operation on the given set or not:

Is * defined by a^(*)b=(a+b)/(2) is binary operation on Z.

Let * be a binary operation on N defined by a*b = a^(b) for all a,b in N show that * is neither commutative nor associative

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.

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

Let * be a binary operation on Z defined by a*b=a+b-4 for all a,b in Z. show that * is both commutative and associative.