Which of the following sets are closed under multiplication? Select all that apply.
1. Integers
2. Natural numbers
3. Irrational numbers

Solution:

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 the set M.

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.

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

Summary:

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