Question

Solve the following problems and verify the data by drawing Venn diagrams. In a group of passengers, $100$ know Kannada, $50$ know English and $25$ know both. If passengers know either Kannada or English, how many passengers are in the group?

Answer 1

Let the total number of passengers who know Kannada be $n\left(K\right)$ and number of passengers who know English be $n\left(E\right)$.

Then, the number of passengers who know both Kannada and English is $n(K\cap E)$.

We know that $n(A\cup B)=n\left(A\right)+n\left(B\right)-n(A\cap B)$ where $A$ and $B$ are the respective sets.

Here, it is given that in a group of passengers, $100$ know Kannada, $50$ know English and $25$ know both, that is $n\left(K\right)=100,n\left(E\right)=50$ and $n(K\cap E)=25$ and therefore,

$n(K\cup E)=n\left(K\right)+n\left(E\right)-n(K\cap E)=100+50-25=150-25=125$

Hence, there are $125$ passengers in the group.