Question

State whether the following statements are true or false. Justify.

If * is a commutative binary operation on N, then a * (b * c) = (c * b) * a

Answer 1

R.H.S. = (c * b) * a

= (b * c) * a [* is commutative]

= a * (b * c) [Again, as * is commutative]

= L.H.S.

∴ a * (b * c) = (c * b) * a

Therefore, statement (ii) is true.