Question

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

A

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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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