Set $A$ has $m$ elements and Set $B$ has $n$ elements. If the total number of subsets of $A$ is $112$ more than the total number of subsets of $B$,then the value of $m \times n$ is

If $A$ and $B$ are two sets,then $A \cup (A \cap B)$ is equal to

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

Make correct statements by filling in the symbols $\subset$ or $\not\subset$ in the blank spaces:
${ x:x \text{ is a circle in the plane} } \dots { x:x \text{ is a circle in the same plane with radius } 1 \text{ unit} }$

The set $\{n(n+1)(2n+1) : n \in \mathbb{Z}\}$ is a subset of:

Match each of the set on the left described in the roster form with the same set on the right described in the set-builder form:

$(i) \{ P,R,I,N,C,A,L\} $	$(a) \{ x:x \text{ is a positive integer and is a divisor of } 18\} $
$(ii) \{ 0\} $	$(b) \{ x:x \text{ is an integer and } x^2 - 9 = 0\} $
$(iii) \{ 1,2,3,6,9,18\} $	$(c) \{ x:x \text{ is an integer and } x + 1 = 1\} $
$(iv) \{ 3, -3\} $	$(d) \{ x:x \text{ is a letter of the word } PRINCIPAL\} $