Write the following as an interval: $\{ x : x \in R, -4 < x \le 6 \}$

Examine whether the following statement is true or false:
$\{a, e\} \subset \{x : x \text{ is a vowel in the English alphabet}\}$

In each of the following,determine whether the statement is true or false. If it is true,prove it. If it is false,give an example.
If $A \subset B$ and $x \notin B,$ then $x \notin A$.

Find sets $A, B$ and $C$ such that $A \cap B, B \cap C$ and $A \cap C$ are non-empty sets and $A \cap B \cap C = \varnothing$.

Two sets $A$ and $B$ are disjoint if and only if

For two sets $A$ and $B$,$A \cup B = A$ if and only if