Question

If $ a\;{\text{and}}\;b $ are whole numbers then which of the following is true?
A. $ a \div b $ is a whole number
B. $ a \div b = b \div a $
C.Both
D.None of these

Answer 1

Hint: In this question, you have to go through each option to check which of them is true. And before going to check all the options, you should know that division operation does not hold good for closure property of rational numbers and also not for commutative property, use this information to find the correct option.

Complete step-by-step answer:
We have given two whole numbers $ a\;{\text{and}}\;b $ and based on which we have asked which of the above options is true. So we will go through each of them one by one,
The first option, which says $ a \div b $ is a whole number, since if we read the properties of whole numbers then we will come to know that closure property does not holds good for division, because we may get a fraction number and what if when we divide with $ 0 $
So, the first option is incorrect.
 Now, the second option, which says $ a \div b = b \div a $ , we know that commutative properties do not hold good for division, therefore this is also an incorrect option.
Third option, which says both, it means first and second are true, so it is also false.
Fourth option, it says none of any option is true, so yes this is true.
So, the correct answer is “Option D”.

Note: If closure property holds good for a set of numbers, like addition between whole numbers, then it means the output of the operation will also belong to the same set, since addition of two whole numbers always gives a whole number.