​$$\text{Let } \{E_n\} \text{ be a sequence of subsets of } \mathbb{R}. \\\text{Define }\\\limsup_{n} E_n = \bigcap_{k=1}^\infty \bigcup_{n=k}^\infty E_n\\\liminf_{n} E_n = \bigcup_{k=1}^\infty \bigcap_{n=k}^\infty E_n\\\text{Which of the following statements is true?}$$​​

Correct option is C

​$$\bigcap_{n=1}^\infty E_n = E_1 \cap E_2 \cap \dots \cap \dots\\\bigcap_{n=2}^\infty E_n = E_2 \cap E_3 \cap \dots \cap \dots\\\bigcap_{n=3}^\infty E_n = E_3 \cap E_4 \cap \dots \cap \dots\\\implies \bigcup_{k=1}^\infty \bigcap_{n=k}^\infty E_n = \liminf_n E_n\\\text{So, } \liminf_n E_n \text{ contains those } x \text{ such that } \\x \in E_n \text{ for all but finitely many } n.$$​​