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