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