Examine whether the following statement is true or false:
$\{a\} \subset \{a, b, c\}$

State which of the following sets are finite or infinite:
$\{ x : x \in \mathbb{N} \text{ and } (x - 1)(x - 2) = 0 \}$

Let $S = \{0, 1, 5, 4, 7\}$. Then the number of all subsets of $S$ is:

In the set-builder notation (rule method),the null set is represented by:

The solution set of $x \equiv 3 \pmod{7}$,where $p \in \mathbb{Z}$,is given by:

In each of the following,determine whether the statement is true or false. If it is true,prove it. If it is false,give a counterexample.
If $x \in A$ and $A \not\subset B$,then $x \in B$