Q. 2 F4.4( 5 Votes )
For each operation ∗ defined below, determine whether ∗ is binary, commutative or associative.
On R – {–1}, define a ∗ b = 
Answer :
It is given that On R, * – {– 1}, define a ∗ b = 
ϵ R for b ≠ -1, so the operation * is binary.
We can see that 1 * 2 = 
and 2 * 1=
⇒ 1 * 2 ≠ 2 * 1; where 1,2 ϵ R – {-1}
⇒ the operation * is not commutative.
Now, we can observed that
(1 * 2) * 3 = 
1 * (2 * 3) = 1 * 
⇒ (1 * 2) * 3 ≠ 1 * (2 * 3), where 1,2,3 ϵ R * – {– 1}
⇒ The operation * is not associative.
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