- On Q, define a ∗ b = ab/2
- On Z+, define a ∗ b = 2ab
(iii) On Q, characterize a ∗ b = stomach muscle/2
Stage 1: Check for commutative
Consider ∗ is commutative, then, at that point a ∗ b = b * a
Which implies, abdominal muscle/2 = ba/2 or stomach muscle/2 = abdominal muscle/2 (which is valid)
a ∗ b = b * a for each of the a, b ∈ Q
In this way, ∗ is commutative.
Stage 2: Check for Associative.
Consider ∗ is cooperative, then, at that point (a ∗ b)* c = a * (b * c)
LHS = (a ∗ b) * c = (stomach muscle/2) * c
???????? ×????
= 2
2
= abc/4
RHS = a * (b * c) = a * (bc/2)
????×????????
= 2
2
= abc/4
This infers LHS = RHS
Accordingly, ∗ is acquainted parallel activity.
(iv) On Z+, characterize a ∗ b = 2ab
Stage 1: Check for commutative
Consider ∗ is commutative, then, at that point a ∗ b = b * a
Which implies, 2ab = 2ba
or then again 2ab = 2ab (which is valid)
a ∗ b = b * a for every one of the a, b ∈ Z+ Therefore, ∗ is commutative. Stage 2: Check for Associative.
Consider ∗ is acquainted, then, at that point
(a ∗ b)* c = a * (b * c)
LHS = (a ∗ b) * c = (2ab ) * c
= 22???????? ????
RHS = a * (b * c) = a * 2bc
= 22???????? ????
This infers LHS ≠ RHS
In this way, ∗ isn’t cooperative paired activity.