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 has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.
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