Solution:
Stage 1: Check for commutative and cooperative for activity *. a * b = |a – b| and b * a = |b – a| = (a, b)
Activity * is commutative.
a(bc) = a|b-c| = |a-(b-c)| = |a-b+c| and (ab)c = |a-b|c = |a-b-c|
In this way, a(bc) ≠ (ab)c
Activity * is cooperative.
Stage 2: Check for commutative and cooperative for activity o. aob = a ∀ a, b ∈ R and boa = b
This infers aob boa
Activity o isn’t commutative.
Once more, an o (b o c) = an o b = an and (aob)oc = aoc = a Here ao(boc) = (aob)oc
Activity o is cooperative.
Stage 3: Check for the distributive properties
In the event that * is distributive over o, RHS:
= LHS
Also, LHS
RHS
LHS ≠ RHS
Henceforth, activity o doesn’t disperse over.