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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

User Fidd
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1 Answer

6 votes

Answer:

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

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

User Martin Lantzsch
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