Q. 12 B3.9( 7 Votes )

# 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 :

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

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