Two finite sets have $m$ and $n$ elements respectively. The total number of subsets of the first set is $56$ more than the total number of subsets of the second set. The values of $m$ and $n$,respectively are

Let $A, B$ and $C$ be three sets. If $A \in B$ and $B \subset C$,is it true that $A \subset C$? If not,give an example.

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

The number of elements in the set $\{ (a, b) : 2a^2 + 3b^2 = 35, a, b \in Z \} $,where $Z$ is the set of all integers,is

If $Q = \{x : x = \frac{1}{y}, y \in N\}$,then which of the following is true?

Find the pairs of equal sets,if any,give reasons:
$A = \{ 0 \}$
$B = \{ x : x > 15 \text{ and } x < 5 \}$
$C = \{ x : x - 5 = 0 \}$
$D = \{ x : x^2 = 25 \}$
$E = \{ x : x \text{ is an integral positive root of the equation } x^2 - 2x - 15 = 0 \}$