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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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