If $A = \{1, 2, 3, 4, 5\}$,then the number of proper subsets of $A$ is

The number of subgroups of the group $(Z_{5}, +_{5})$ is

Consider the experiment of rolling a die. Let $A$ be the event 'getting a prime number' and $B$ be the event 'getting an odd number'. Write the sets representing the events $A$ and $B$.

Let $A = \{1, 2, \{3, 4\}, 5\}$. Which of the following statements is incorrect and why?
$\{\varnothing\} \subset A$

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

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\} $