Determine whether or not the definition of * given below gives a binary operation. In the event that * is not a binary operation give justification of this.(iii) On R, define * by ab = ab2 (iv) On Z+ define by a * b = |a − b|

contexto.140

3 years ago

(iii) Since, on R, define by a*b = ab²

Let

Thus, * is a binary operation on R.

(iv) Given on Z⁺ define * by a * b = |a − b|

Let

Therefore,

a * b ∈ Z⁺, ∀ a, b ∈ Z⁺

Thus, * is a binary operation on Z⁺.