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# State whether the following statement is true or false. Justify. ii) If $\ast$ is a commutative binary operation on N, then $a \ast (b \ast c) = (c \ast b) \ast a$.

Toolbox:
• An operation $\ast$ on $A$ is commutative if $a\ast b = b \ast a\; \forall \; a, b \in A$
Given binary operator $\ast$ on set $N$. We need to prove that $a \ast (b \ast c) = (c \ast b) \ast a$.
An operation $\ast$ on $A$ is commutative if $a\ast b = b \ast a\; \forall \; a, b \in A$
Therefore $a \ast (b \ast c) = (b \ast c) \ast a$ since $\ast$ is commutative.
Therefore, the statement is true.

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