Question

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

Answer 1

Step-by-step explanation:

i)Given a∗a=a∀aϵN on a set N for an arbitary binary operation ∗.

The binary operation can be defined as,a×b=a

2

Clearly a

2



=a∀aϵA.Therefore the statement is false.

ii)Given binary operator ∗ on set N.We need to prove that a∗(b∗a)=(c∗b)∗a

An operation ∗ on A is commutative

if a∗b=b∗a∀a,bϵA

∴a∗(b∗a)=(c∗b)∗a

since ∗ is commutative.

∴the statement is true.

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