Determine whether or not each of the definition of given below gives a binary operation. In the event that * is not a binary operation, give justification for this. (i) `O n Z^+, d efin e *b ya*b = a - b`(ii) `O n Z^+,

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

Determine whether or not each of the definition 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

Determine whether or not each of the defination 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 defination 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 definition of given below gives a binary operation. In the event that * is not a binary operation, give justification for this. (i) On Z^+ , define ∗ by a ∗ b = a – b (ii) On Z^+ , define ∗ by a ∗ b = ab (iii) On R , define ∗ by a ∗ b = ab^2 (iv) On Z^+ , define ∗ by a ∗ b = |a – b| (v) On Z^+ , define ∗ by a ∗ b = a

Determine whether or not each of the definition of given below gives a binary operation. In the event that * is not a binary operation, give justification for this. (i) On Z^+ , define ∗ by a ∗ b = a – b (ii) On Z^+ , define ∗ by a ∗ b = ab (iii) On R , define ∗ by a ∗ b = ab^2 (iv) On Z^+ , define ∗ by a ∗ b = |a – b| (v) On Z^+ , define ∗ by a ∗ b = a

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|