Which of the following gives an example of a set that is closed under addition?

A) The sum of an odd number and an odd number

B) The sum of a multiple of 3 and a multiple of 3

C) The sum of a prime number and a prime number

D) None of these are an example of the closure property

The sum of a multiple of 3 and a multiple of 3 gives an example of a set that is closed under addition ⇒ B

Step-by-step explanation:

A set is closed under addition if we add any members of the set and the answer is belong to the set

Let us check each answer:

A.

The set of odd numbers is { ..., - 3, - 1, 1, 3, 5, 7, ... }

∵ - 3 + - 1 = - 4 ⇒ even number

- The answer does not belong to the set of odd numbers

∴ - 4 ∉ set of odd numbers

The sum of an odd number and an odd number does not give an example of a set that is closed under addition

B.

The set of multiplies of 3 is { ..., - 9, - 3, 0, 3, 9, 6, ... }

∵ - 9 + - 3 = - 12 ⇒ multiple of 3

∵ - 3 + 3 = 0 ⇒ multiple of 3

∵ - 9 + 6 = - 3 ⇒ multiple of 3

- That means the sum of any two multiplies of 3 is a multiple of 3

∴ - 12, 0, - 3 ∈ set of multiplies of 3

The sum of a multiple of 3 and a multiple of 3 gives an example of a set that is closed under addition

C. The set of prime numbers is {2, 3, 5, 7, 11, 13, 17, ... }

∵ 3 + 5 = 8 ⇒ not prime number

- The answer does not belong to the set of prime numbers

∴ 8 ∉ set of prime numbers

The sum of a prime number and a prime number does not give an example of a set that is closed under addition

The sum of a multiple of 3 and a multiple of 3 gives an example of a set that is closed under addition