If $aN = \{ ax : x \in N \}$,then the set $3N \cap 7N$ is .....$N$.

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 $x \notin A$.

If $Q = \{x : x = \frac{1}{y}, \text{ where } y \in N\}$,then which of the following is true?

How many elements does $P(A)$ have,if $A = \varnothing$?

Make correct statements by filling in the symbols $\subset$ or $\not\subset$ in the blank spaces:
${ x:x \text{ is an equilateral triangle in a plane} } \dots { x:x \text{ is a triangle in the same plane} }$

If a set $A$ has $n$ elements, then the total number of subsets of $A$ is