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

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

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\} $

If $A, B$,and $C$ are three sets,then $A \times (B \cup C)$ is equal to

In a city,no two persons have an identical set of teeth,and there is no person without a tooth. Also,no person has more than $32$ teeth. If we disregard the shape and size of the teeth and consider only the presence or absence of a tooth at each of the $32$ positions,then the maximum population of the city is:

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