Mark the tick against the correct answer in the following:
Let Z+ be the set of all positive integers. Then, the operation * on Z+ defined by
a * b = ab is
According to the question ,
Q = { All integers }
R = {(a, b) : a * b = ab }
Formula
* is commutative if a * b = b * a
* is associative if (a * b) * c = a * (b * c)
Check for commutative
Consider , a * b = ab
And , b * a = ba
Both equations are not the same and will not always be true .
Therefore , * is not commutative ……. (1)
Check for associative
Consider , (a * b) * c = (ab) * c =
And , a * (b * c) = a * (bc)=
Ex a=2 b=3 c=4
(a * b) * c = (23) * c =
a * (b * c) = 2 * (34)=
Both the equation are not the same and therefore will not always be true.
Therefore , * is not associative ……. (2)
Now , according to the equations (1) , (2)
Correct option will be (C)