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Question

State whether the following statements are true of false. Justify.
(i) For an arbitrary binary operation on as set N,aa=aaϵN
(ii) If is a commutative binary operation on N, then a(bc)=(cb)a

A
True
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B
False
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Solution

The correct option is A True
i)Given aa=aaϵN on a set N for an arbitary binary operation .
The binary operation can be defined as,a×b=a2
Clearly a2aaϵA.Therefore the statement is false.
ii)Given binary operator on set N.We need to prove that a(ba)=(cb)a
An operation on A is commutative
if ab=baa,bϵA
a(ba)=(cb)a
since is commutative.
the statement is true.

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