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

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

i would need to see the dot plot : )