Final answer:
The set of all integers is closed under addition because adding any two integers will result in another integer. This is true for all integers, making it irrelevant whether a specific integer like -14 or 7 is mentioned.
The correct option is c.
Step-by-step explanation:
The question asks whether the set of all integers is closed under addition. A set is considered closed under an operation such as addition if, when you apply the operation to any two elements in the set, the result is also an element of that set. In the case of the set of all integers, this is indeed the case. No matter which two integers you select and add together, the result will always be an integer as well. Therefore, the correct answer is:
c. Yes, because -20 is in the set.
This is true not just for -20 but for all integers. Adding two integers always results in another integer. This is also supported by the commutative property of addition (A+B=B+A), which is valid for any two integers A and B. As an example, adding -14 (an integer) and 14 (another integer) results in 0, which is yet another integer, showing that the set is closed under addition.
However, if we look at the given options in the context of this question, neither -14 nor 7 is relevant to determine whether the set of all integers is closed under addition since their presence or absence in a subset does not affect the overall property of the integer set. Therefore, the mentions of -14 and 7 in options a, b, and d are red herrings in this context.
The correct option is c.