True or false statements

Question

Two of the following statements are true and one is false

a) For all rational numbers $q$, there exists an integer $n$ so that $q+n=271$.
b) For all integers $n$, there exists a rational number $q$ so that $q+n=271$.
c) There exists an integer $n$ so that $271-n$ is even.

I believe a and c are true and b is false

Answer 1

Hints:

• For any integers $x$ and $y$, their difference $x-y$ is an integer.

• Every integer is a rational number.

• $\frac{1}{2}$ is a rational number.