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# State whether the following statements are true or false. Justify. For an arbitrary binary operation ∗ on a set N, a ∗ a = a ∀ a ∈ N.

Q.12 State whether the following statements are true or false. Justify.

(i) For an arbitrary binary operation ∗ on a set N,$a*a = a,\; \forall a\in N$

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(i) For an arbitrary binary operation ∗ on a set N,$a*a = a,\; \forall a\in N$

An operation * on a set N as $a*b=a+b\, \, \, \, \forall\, \, a,b \in N$

Then , for  b=a=2

$2*2= 2+2 = 4\neq 2$

Hence, statement (i) is false.

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