cmi-entrance 2016 Q7

cmi-entrance · India · pgmath 4 marks Number Theory Combinatorial Number Theory and Counting
Let $U \subseteq \mathbb{R}$ be a non-empty open subset. Choose the correct statement(s) from below:
(A) $U$ is uncountable;
(B) $U$ contains a closed interval as a proper subset;
(C) $U$ is a countable union of disjoint open intervals;
(D) $U$ contains a convergent sequence of real numbers.
Let $U \subseteq \mathbb{R}$ be a non-empty open subset. Choose the correct statement(s) from below:\\
(A) $U$ is uncountable;\\
(B) $U$ contains a closed interval as a proper subset;\\
(C) $U$ is a countable union of disjoint open intervals;\\
(D) $U$ contains a convergent sequence of real numbers.