Choose whether the given statement is true or false.

If a and b are two odd primes, then it is true that is composite.

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False

True

answer is B.

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Detailed Solution

We know that

…………………..(1).
From the question, it is clear that a and b are two odd primes.
We know that the difference between two odd numbers is equal to an even number. So, we can say that a − b is an even number.
We also know that the sum of two odd numbers are equal to an even number.
So, we can say that a + b is an even number.
We know that the product of two even numbers is an even number.
So, we can say that the product of a − b and a + b
is also an even number.
From equation (1), we can say that

is an even number.
We can also say as both a – b and a + b are even numbers, then the product of a – b and a + b is a multiple of 2.
We know that a prime number is a number whose factors are 1 and itself.
So, we can say that that

is a composite number.
Hence, the given statement is true.

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