Question

In the Venn diagram, the universal set, $\xi =\left\{\text{students in class 8}\right\}$, set $M=\left\{\text{students who passed mathematics}\right\}$ and set $N=\left\{\text{students who passed English}\right\}$.
It is given that $n\left(M\right)=50,n\left(N\right)=60$ and $n(M\cap N)=12$. If $2$ students failed both subjects, find the total number of students who sat for the examination

• A. $98$
• B. $100$
• C. $112$
• D. $120$

Answer 1

The correct option is B $100$

M= {Students who passed Mathematics}

N= {Students who passed English}

$n\left(M\right)=50,n\left(N\right)=60$

$n(M\cap N)=12$

$n(M\cup N)=n\left(M\right)+n\left(N\right)-n(M\cap N)=50+60-12=98$

$n\left(U\right)=$ n(Passed in Maths or English) $+$ n (Failed in Maths and English)

$n\left(U\right)=98+2=100$