# Which of the following sets are closed under division?

1) integers 2) irrational numbers 3) whole numbers

The closure property of division states that if A, B are the two numbers that belong to a Set X then A ÷ B = C also belongs to set X.

## Answer: Integers, Irrational numbers, and Whole numbers - None of these sets are closed under division.

Let us understand the concept of closure property.

**Explanation:**

Let a, b ∈ Z [ Z denoted the set of integers]

If a = 1, b = 0

1 / 0 ∉ Z

Thus, a ÷ b = a/ b ∉ Z

Thus, Integers are not closed under division.

Let's take and irrational number √2

√2 ∈ Q [Q is the set of irrational numbers]

Then, √2 ÷ √2 = 1 ∉ Q [Since, 1 is a rational number]

Thus, Irrational numbers are not closed under division.

Let a, b ∈ W [W is a set of whole numbers]

If a = 3, b = 0

3 / 0 ∉ W

Thus, a ÷ b = a/ b ∉ W.

Hence, Whole Numbers are not closed under division.