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

Write the following set in the set-builder form: $\{ 2, 4, 6, \dots \}$

If $A = \{1, 2, 3, 4, 5, 6\}$, then which of the following statements is false?

Which of the following sets is finite or infinite?
The set of prime numbers less than $99$.

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 $B \subset C$,then $A \subset C$.

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 $A \not\subset B$ and $B \not\subset C$,then $A \not\subset C$.