For each binary * operation defined below,determine * whether is commu

1.	For each binary * operation defined below,determine * whether is commutative or associative.On Q, define a*b = ab + 1
Answer» a ∈ Q, b ∈ Q a * b = ab + 1 b * a = ab + 1 ∴ a * b = b * a, hence commutative ( a * b )c = (ab+1) c = (ab + 1) c + 1 = abc + c + 1 a(bc) = a* (bc + 1) = a (bc + 1) + 1 = abc + a + 1 ∴ (a * b) c a* (b * c) hence * is not associative

For each binary * operation defined below,determine * whether is commutative or associative.On Q, define a*b = ab + 1

Answer»

a ∈ Q, b ∈ Q

a * b = ab + 1

b * a = ab + 1

∴ a * b = b * a, hence commutative

( a * b )*c = (ab+1) *c

= (ab + 1) c + 1

= abc + c + 1 a*(b*c)

= a* (bc + 1)

= a (bc + 1) + 1

= abc + a + 1

∴ (a * b) *c * a* (b * c)

hence * is not associative