- Is ∗ associative?
- Find the identity of ∗ in N
(iii) Is ∗ affiliated?
For a,b, c ∈ N
(a ∗ b) * c = (L.C.M. of an and b) * c = L.C.M. of a, b and c a ∗ (b * c) = a * (L.C.M. of b and c) = L.C.M. of a, b and c (a ∗ b) * c = a ∗ (b * c)
Along these lines, activity ∗ cooperative.
(iv) Find the character of ∗ in N
Character of * in N = 1
since a * 1 = L.C.M. of an and 1 = a