Sachchidanand Prasad

12-04-2025

Problem: Let $X$ be a connected subset of real numbers. If every element of $X$ is irrational, then the cardinality of $X$ is .

Choose an answer to see the solution.

miscellaneous MCQ
Solution: Given that $X \subseteq \mathbb{R} $ is connected and contains only irrational numbers. We know that the only set which are connected in $\mathbb{R} $ are intervals. Since $X$ contains only irrational numbers, it must be singleton set. Thus, the cardinality of $X$ is $1$. Therefore, the correct option is (D).

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