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

If $D_{30}$ is the set of all divisors of $30$,$x, y \in D_{30}$,we define $x+y=\operatorname{LCM}(x, y)$,$x \cdot y=\operatorname{GCD}(x, y)$,$x^{\prime}=\frac{30}{x}$ and $f(x, y, z)=(x+y) \cdot (y^{\prime}+z)$,then $f(2, 5, 15)$ is equal to

Decide,among the following sets,which sets are subsets of one another:
$A = \{ x: x \in \mathbb{R} \text{ and } x \text{ satisfies } x^2 - 8x + 12 = 0 \},$
$B = \{2, 4, 6\}, C = \{2, 4, 6, 8, \dots\}, D = \{6\}$

Let $A$ and $B$ be two sets. Then

Let $A = \{a, e, i, o, u\}$ and $B = \{a, b, c, d\}$. Is $A$ a subset of $B$? No. (Why?). Is $B$ a subset of $A$? No. (Why?)