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

Let $A, B,$ and $C$ be sets such that $A \cup B = A \cup C$ and $A \cap B = A \cap C$. Show that $B = C$.

In the following,state whether $A=B$ or not:
$A=\{a, b, c, d\} ; B=\{d, c, b, a\}$

Let $a > 0, a \neq 1$. Then,the set $S$ of all positive real numbers $b$ satisfying $(1+a^2)(1+b^2) = 4ab$ is

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 following pair of sets: $\phi \dots B$.

Let $A = \{1, 2, 3, 4, 5, 6\}$. Insert the appropriate symbol $\in$ or $\notin$ in the blank space:
$10 \dots A$