Show that * on Z + defined by a *b = |a –b| is not a binary operation.

Question

Philoid · Accepted Answer

To prove: * is not a binary operation

Given: a and b are defined on positive integer set

And a*b = |a - b|

⇒ a*b = (a - b), when a>b

= b - a when b>a

= 0 when a = b

But 0 is neither positive nor negative.

So 0 does not belong to Z ⁺ .

So a*b = |a - b| does not belong to Z ⁺ for all values of a and b

So * is not a binary operation.

Hence proved