Is the set of multiples of 4 closed under addition? Explain why or provide a counterexample if not.

A.
Yes, because the sum of any two multiples of 4 is also a multiple of 4.

B.
Yes, because the sum of any two multiples of 4 is also a multiple of 8.

C.
No, and a counterexample is –4 + (–8) = –12.

D.
No, and a counterexample is 26 + 16 = 42.

Question

Is the set of multiples of 4 closed under addition? Explain why or provide a counterexample if not.
 
 A.
Yes, because the sum of any two multiples of 4 is also a multiple of 4.
 
 B.
Yes, because the sum of any two multiples of 4 is also a multiple of 8.
 
 C.
No, and a counterexample is –4 + (–8) = –12.
 
 D.
No, and a counterexample is 26 + 16 = 42.

ddcamp · Answer

If the set is closed under addition, then it means that adding any two numbers in the set will never give something not in the set.

If the set of multiples of four is closed under addition, it means that you can't get something that's not a multiple of four by adding multiples of four. Is this true?