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

1.	For each binary * operation defined below,determine * whether is commutative or associative.On Z, define a * b = a – b
Answer» a = 3, b = 2, a – b = 3 – 2= 1 b-a = 2-3 = -1 a – b ≠ b – a, hence not commutative a = 3, b = 2, c = 1 (a * b) * c = (3 – 2) * 1 = 1 * 1 = 0 a(b c) = 3* (2 * 1) = 3(2 – 1) = 3 1 = 3 – 1 = 2 (a * b) * c ≠ a * (b * c), hence * is not associative

For each binary * operation defined below,determine * whether is commutative or associative.On Z, define a * b = a – b

Answer»

a = 3, b = 2,

a – b = 3 – 2= 1

b-a = 2-3 = -1

a – b ≠ b – a,

hence not commutative

a = 3, b = 2, c = 1

(a * b) * c = (3 – 2) * 1

= 1 * 1 = 0

a*(b * c) = 3* (2 * 1)

= 3*(2 – 1) = 3 * 1

= 3 – 1 = 2

(a * b) * c ≠ a * (b * c),

hence * is not associative