Q. 205.0( 1 Vote )

Mark the tick aga

Answer :

According to the question ,


Q = { All integers }


R = {(a, b) : 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 = a + b - ab


And , b * a = b + a - ba


Both equations are the same and will always be true .


Therefore , * is commutative ……. (1)


Check for associative


Consider , (a * b) * c = (a + b - ab) * c


= a + b - ab + c -(a + b - ab)c


=a + b – ab + c – ac – bc + abc


And , a * (b * c) = a * (b + c - bc)


= a + (b + c - bc) - a(b + c - bc)


=a + b + c – bc - ab – ac + abc


Both the equation are the same and therefore will always be true.


Therefore , * is associative ……. (2)


Now , according to the equations (1) , (2)


Correct option will be (D)

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