Q12 of 107 Page 24

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

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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