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Solution :

In `Z^(+), a ** b =a - b` <br> `2**3 = 2-3 = -1 in Z^(+)` <br> `therefore` Given operation is not binary. <br> (ii) In `Z^(+), a ** b = ab` <br> The product of every two positive intergers is a positive interger. <br> `therefore` Given operations is binary. <br> (iii) In R, `a ** b= ab^(2)` <br> The square of every real number is always a real number. <br> (iv) In `Z^(+) , " "a**b = a` <br> The modulus of the difference of every two positive integer. <br> `therefore` Given operation in binary. <br> (v) `In Z^(+), " " a**b=a` <br> For each `a,b in Z^(+)` <br> `" "a * b = a in Z^(+)` <br> `therefore` Given operation is binary.