Q. 215.0( 1 Vote )

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Answer :

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)

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