1. a ∗ b = ab/4
2. a ∗ b = ab2

(v) a ∗ b = abdominal muscle/4

b * a = ba/2 = abdominal muscle/2 a ∗ b = b * a

The activity * is commutative. Check for affiliated:

(a * b) * c = abdominal muscle/4 * c = abc/16 a * (b *c) = a * (bc/4) = abc/16 (a * b) * c = a * (b *c)

The activity * is acquainted.

(vi) a ∗ b = ab2

b ∗ a = ba2

a ∗ b ≠ b ∗ a

The activity * isn’t commutative. Check for cooperative:

(a * b) * c = (ab2 ) * c = ab2 c2 a * (b *c) = a * (b c2 ) = ab2 c4 (a * b) * c ≠ a * (b *c)

The activity * isn’t cooperative.