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

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

Philoid · Accepted Answer

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

The above statement if true.

Explanation: RHS = (c * b) * a

= (b * c) * a (* is commutative)

= a * (b * c) (as * is commutative)

= LHS.

Therefore, a * (b * c) = (c * b) * a.

Hence Proved

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