1. a ∗ b = a + ab
2. a ∗ b = (a – b)2

(iii) a ∗ b = a + stomach muscle

a ∗ b = a + stomach muscle = a(1 + b) b * a = b + ba = b (1+a)

a ∗ b ≠ b * a

The activity * isn’t commutative Check for cooperative:

(a * b) * c = (a + stomach muscle) * c = (a + stomach muscle) + (a + ab)c a * (b *c) = a * (b + bc ) = a + a(b + bc)

(a * b) * c ≠ a * (b *c)

The activity * isn’t acquainted

(iv) a ∗ b = (a – b)2

a ∗ b = (a – b)2 b * a = (b – a)2

a ∗ b = b * a

The activity * is commutative.

Check for acquainted:

(a * b) * c = (a – b)2 * c = ((a – b)2 – c)2

a * (b *c) = a * (b – c )2 = (a – (b – c)2 )2

(a * b) * c ≠ a * (b *c)

The activity * isn’t affiliated