Mark the tick against the correct answer in the following:
Let a * b = a + ab for all a, b ∈ Q. Then,
According to the question ,
Q = { a,b }
R = {(a, b) : a * b = a + ab }
Formula
* is commutative if a * b = b * a
* is associative if (a * b) * c = a * (b * c)
Check for commutative
Consider , a * b = a + ab
And , b * a = b + ba
Both equations will not always be true .
Therefore , * is not commutative ……. (1)
Check for associative
Consider , (a * b) * c = (a + ab) * c = a+ab + (a+ab)c=a+ab+ac+abc
And , a * (b * c) = a * (b+bc) = a+a(b+bc) = a+ab+abc
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 (B)