Mark the tick against the correct answer in the following:
Let Q be the set of all rational numbers, and * be the binary operation, defined by a * b = a + 2b, then
According to the question ,
Q is set of all rarional numbers
R = {(a, b) : a * b = a + 2b }
Formula
* is commutative if a * b = b * a
* is associative if (a * b) * c = a * (b * c)
Check for commutative
Consider , a * b = a + 2b
And , b * a = b + 2a
Both equations will not always be true .
Therefore , * is not commutative ……. (1)
Check for associative
Consider , (a * b) * c = (a + 2b) * c = a+2b + 2c
And , a * (b * c) = a * (b+2c) = a+2(b+2c) = a+2b+4c
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)