The Total solution for NCERT class 6-12
On the set Z of integers a binary operation * is defined by a 8 b = ab +1 for all a, b ∈ Z. Prove that * is not associative onZ.
Let a, b, c ∈ Z
a * (b * c) = a * (bc+ 1)
= a (bc + 1) + 1
= a b c + a + 1
(a * b) * c = (ab+ 1)* c
= (ab + 1) c + 1
= a b c + c + 1
Thus, a * (b * c) ≠ (a* b) * c
Thus, * is notassociative on Z.