Let $$S$$ be a set of all distinct numbers of the form $$\frac{P}{Q},$$ where $$p,\,q,\, \in \left\{ {1,\,2,\,3,\,4,\,5,\,6} \right\}.$$ What is the cardinality of the set $$S$$ ?
A.
21
B.
23
C.
32
D.
36
Answer :
36
Solution :
Number of elements given $$ = 6$$
Number of elements taken at a time $$ = 2{\text{ i}}{\text{.e}}{\text{.,}}\left( {p\,\& \,q} \right)$$
$$ \Rightarrow $$ Cardinality of the set $$\left( s \right) = {6^2} = 36$$
(because numbers are repeated).
Releted MCQ Question on Calculus >> Sets and Relations
Releted Question 1
If $$X$$ and $$Y$$ are two sets, then $$X \cap {\left( {X \cup Y} \right)^c}$$ equals.