Answer to Question #308335 in Real Analysis for Pankaj

Question

Which of the following statements are true and which are false? Justify your answers with

a short proof or a counter-example:

For every finite set S, S ∈ S

Answer 1

The statement is false. Let $S=\{1\}$ . Since $\{1\}\notin {1}$ , we have$S\notin S$ .