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.
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.
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.