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Commutative Law of Binary Operation

State whether...

Question

State whether the given below statement is true or false. Justify.

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

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Solution

$To check:$ If $$ is a commutative binary

operation on $N,$ then $a (b * c) = (c * b) * a$

Solving R.H.S.,

$R . H . S . = (c * b) * a$

$= (b * c) * a (∴ * is commutative)$

$= a * (b * c) (∴ * is commutative)$

$= L . H . S$

$∴ a * (b * c) = (c * b) * a$

Thus, statement is true.

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Commutative Law of Binary Operation

Standard IX Mathematics

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