Consider the sets $\phi, A = \{1, 3\}, B = \{1, 5, 9\}, C = \{1, 3, 5, 7, 9\}$. Insert the symbol $\subset$ or $\not\subset$ between the pair of sets: $B \dots C$.

The number of proper subsets of the set $\{1, 2, 3\}$ is

If $A = \{ x : x \text{ is a natural number} \}$,$B = \{ x : x \text{ is an even natural number} \}$,$C = \{ x : x \text{ is an odd natural number} \}$,and $D = \{ x : x \text{ is a prime number} \}$,find $A \cap D$.

Make correct statements by filling in the symbols $\subset$ or $\not\subset$ in the blank spaces:
${ x:x \text{ is an even natural number} } \dots { x:x \text{ is an integer} }$

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 $A \not\subset C$.

Which of the following is an empty set?