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Question

Which of the following is not a binary operation defined on the set of positive real numbers?


A

Addition

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B

Subtraction

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C

Division

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D

Multiplication

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Solution

The correct option is B

Subtraction


In a binary operation we take two inputs from the same set and get an output from the

same set. If we add two positive numbers we always get a positive number. We can say that addition is a

binary operation from set of positive numbers to set of positive numbers.

We know that for two positive numbers ‘a’ and ‘b’, a-b will be negative if b is greater than a. It means for

subtraction defined on the set of positive numbers, output may be a negative number. But for a binary

operation, both input and output should be from the same set.

Both multiplication and division of two numbers p and q(pq and pq)will give only positive numbers if p

and q are positive. So we can say both are valid binary operation defined on the set of positive numbers.

So the correct answer is B


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