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Byju's Answer

Standard IX

Mathematics

Venn Diagram

In the Venn d...

Question

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

98

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100

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112

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120

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Solution

The correct option is D $100$
Hence by set theory

$n (N \cup M) = n (N) + n (M) - n (N \cap M)$

$= 50 + 60 - 12 = 98$

$2$ students failed while $98$ passed in at least one of given subjects.

Hence $100$ students sat for the examination.

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In the Venn diagram, the universal set, ξ= {students in class 8} set M = {students who passed mathematics} and set N = {students who passed English}.It is given that n(M)=50,n(N)=60 and n(M ∩ N)=12.If 2 students failed bothsubjects, find the total number of students who sat for the examination

The correct option is D 100Hence by set theoryn(N∪M)=n(N)+n(M)−n(N∩M)=50+60−12=982 students failed while 98 passed in at least one of given subjects.Hence 100 students sat for the examination.

The correct option is D $100$
Hence by set theory

$n (N \cup M) = n (N) + n (M) - n (N \cap M)$

$= 50 + 60 - 12 = 98$

$2$ students failed while $98$ passed in at least one of given subjects.

Hence $100$ students sat for the examination.