Question 4
Determine whether the binary operation * on the set N of natural numbers defined by a*b = 2ab is associative or not.
* is associative if
(a * b) * c = a * (b * c)
Since (a * b) * c a * (b * c)
* is not an associative binary operation
(a * b)* c
= (2^ ) * c
= 2^( (2 ^ ) )
a * (b * c)
= a * (2^ )
= 2^( (2^ ))
Note: You can take an example as well Find (1 * 2) * 3 & 1 * (2 * 3), and prove them not equal

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 8 years. He provides courses for Maths and Science at Teachoo. You can check his NCERT Solutions from Class 6 to 12.