Q. 215.0( 1 Vote )

# 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 bya * b = ab isA. commutative but not associativeB. associative but not commutativeC. neither commutative nor associativeD. both commutative and associative

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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