Question

This integer is even if, and only if, it equals twice some integer.

a. If this integer is even, then it does not equal twice some integer, or if this integer does not equal twice some integer, then it is even.
b. If this integer is even, then it does not equal twice some integer, and if this integer does not equal twice some integer, then it is even.
c. If this integer is odd, then it equals twice some integer, or if this integer equals twice some integer, then it is odd.
d. If this integer is even, then it equals twice some integer, or if this integer equals twice some integer, then it is even.
e. If this integer is even, then it equals twice some integer, and if this integer equals twice some integer, then it is even.

Answer 1

The correct option is d. If an integer is even, then it equals twice some integer, and if an integer equals twice some integer, then it is even.

Step-by-step explanation:

The correct statement is option d. If this integer is even, then it equals twice some integer, or if this integer equals twice some integer, then it is even.

An even integer is a number that can be divided evenly by 2. If an integer can be written as 2 times another integer, then it is even. On the other hand, if an integer is even, then it can be written as 2 times some integer. Therefore, option d correctly represents the condition for an integer to be even.