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

Show that if $A \subset B$,then $(C - B) \subset (C - A)$.

The set $A = \{ x : x \ne x \}$ represents:

Which of the following is a set? Justify your answer.
$A$ collection of novels written by the writer Munshi Prem Chand.

Which of the following is a set? Justify your answer.
The collection of all boys in your class.

Let $A$ and $B$ be sets. If $A \cap X = B \cap X = \phi$ and $A \cup X = B \cup X$ for some set $X$,show that $A = B$. (Hint: Use $A = A \cap (A \cup X)$,$B = B \cap (B \cup X)$ and the Distributive law.)