Set theory | TOMATO ISI B.stat Objective | Problem 53

There were  41 candidates in an examination and each candidate was examined in algebra, geometry and calculus. It was found that 12 candidates failed in algebra, 7 failed in geometry and 8 failed in calculus , 2 in geometry  and calculus , 3 in calculus and algebra , 6 in algebra and geometry, whereas  only  1 failed in one of the three  subjects. Then, find  the number of candidates  who passed in all three subjects?

use set theory concept

Can you now finish the problem ..........

we assume that A ,G,C be the sets of the students who failed on algebra ,geometry and calculus respectively.

Find the complement of \(N(A \cup G \cup C)\)

can you finish the problem........

Let S be the set of total students i.e N(s) = 41

we assume that A ,G,C be the sets of the students who failed on algebra ,geometry and calculus respectively.

Therefore

N(A)=12

N(G)=7

N(C)=8

and

\(N(A \cap G \cap C)\)=1

\(N(G \cap C)\) =2 ,

\(N(C\cap A)\) =3

\(N(A\cap G)\) =6

\(N(A \cup G \cup C)\)=\(N(A) + N(G) +N(C) -N(G \cap C) -N (C \cap A) -N(C \cap A) + N(A \cap G \cap C)\)=12 + 7+8-2-6-3+1=17

Therefore complement of \(N(A \cup G \cup C)\) =41-17=24

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