Let $A$ be a subset of real numbers containing all the rational numbers. Which of the following statements is true?
a. $A$ is countable.
b. If $A$ is uncountable then $A=R$.
c. If $A$ is open, then $A=R$.
d. None of the above statement is true.
(a) can't be true since $A$ containing all the rational numbers no way implies that $A$ contains only the rational numbers.
The confusion lies between (b) and (c).