Kenneth Rosen 2.1

Question

Determine True or False

$a)x\varepsilon \left \{ x \right \}$

$b)\left \{ x \right \}\subseteq \left \{ x \right \}$

$c)\left \{ x \right \}\varepsilon \left \{ x \right \}$

Comments

a) True  -  $x$ is an element that belong to a set which contains only one element $\{x\}$.

b) True - A set is always subset of itself.

c) False - It is saying that set $\{x\}$ belong to a set $\{x\}$ which is false. It would be correct if $\{x\} \in  \{\{x\}\}$.