If $$X$$ and $$Y$$ are two sets such that $$\left( {X \cup Y} \right)$$ has $$60$$ elements, $$X$$ has $$38$$ elements and $$Y$$ has $$42$$ elements, how many elements does $$\left( {X \cap Y} \right)$$ have ?
A.
11
B.
20
C.
13
D.
none of these
Answer :
20
Solution :
Since, $$\left( {X \cup Y} \right)$$ has 60 elements, $$X$$ has 38 elements and $$Y$$ has 42 elements.
We know that
$$\eqalign{
& \left( {X \cup Y} \right) = X + Y - X \cap Y \cr
& {\text{or,}}\,\,60 = 38 + 42 - \left( {X \cap Y} \right) \cr
& {\text{or,}}\,\,\left( {X \cap Y} \right) = 80 - 60 = 20 \cr} $$
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.