Question

If p, q and r are integers, then which of the following is not necessarily an integer?

• A. $r÷(p+q)$
• B. $(p-r)\times (r-q)$
• C. $(p-q)+r$
• D. $(p+q)\times r$

Answer 1

The correct option is A $r÷(p+q)$

Closure property holds true for addition, subtraction and multiplication, but not for division.

Here, $(p+q)$ is an integer by closure property of addition and $(p+q)\times r$ is also an integer by closure property of multiplication.

Similarly, $(p-q)+r$ and $(p-r)\times (r-q)$ are integers, but $r÷(p+q)$ might not be an integer.