If $A = \{1, 2, 3, \ldots, 10\}$,then the number of non-empty subsets of $A$ containing only odd numbers 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

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

Which of the following is a set? Justify your answer.
The collection of all even integers.

Show that $A \cap B = A \cap C$ does not necessarily imply $B = C$.

Which of the following sets is finite or infinite?
The set of prime numbers less than $99$.