Which of the Following Sets Are Closed Under Multiplication? Select All That Apply.


Question: Which of the following sets are closed under multiplication? Select all that apply.

1. Integers
2. Natural numbers
3. Irrational numbers

The closure property of multiplication states that if A, B are the two numbers that belong to a set M then A × B =  C also belongs to set M.

Answer: Integers and Natural numbers are the sets that are closed under multiplication.

Let us understand the concept of closure property.

Explanation

Let a, b ∈ N then a × b = ab ∈ N.

Hence, Natural numbers are closed under multiplication. 

a, b ∈ Z then a × b = ab ∈ Z

Hence, Integers are closed under multiplication.

√3 ∈ Q’ then √3 × √3 = 3 ∉ Q’

Hence, Irrational numbers are not closed under multiplication.

Therefore, Integers and Natural numbers are the sets that are closed under multiplication.