Question

Verify whether the operation * defined on Q by a*b = ab/2 is associative or not.

Answer 1

* is defined on Q by a*b = ab/2 for associative we have to prove that a* (b* c) = (a* b)* c 

∴ a*(b*c) = a * ab/2 b*c = bc/2 

= abc/4  ……….. (1) 

(a*b)*c = ab/2 *c 

= abc/4 ……….. (2) 

∴ from (1) and (2) 

∴ * is Associative

∴ * Satisfies the associative property.