Question

Solve the following problems and verify the data in each case by drawing Venn diagrams. In a class, $50$ students offered Mathematics, $42$ offered Biology and $24$ offered both the subjects. Find the total number of students in the class.

Answer 1

Let the total number of students who offered mathematics be $n\left(M\right)$ and number of students who offered biology be $n\left(B\right)$.

Then, the number of students who offered both mathematics and biology is $n(M\cap B)$.

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 class, $50$ students offered mathematics, $42$ offered biology and $24$ offered both the subjects, that is $n\left(M\right)=50,n\left(B\right)=42$ and $n(M\cap B)=24$ and therefore,

$n(M\cup B)=n\left(M\right)+n\left(B\right)-n(M\cap B)=50+42-24=92-24=68$

Hence, the total number of students in the class is $68$.