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

Try this beautiful problem Based on Set Theory useful for ISI B.Stat Entrance.

## Set Theory| ISI B.Stat Entrance | 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?

• $24$
• $26$
• $28$

### Key Concepts

SET

Algebra

Cardinal number

Answer: $24$

TOMATO, Problem 53

Challenges and Thrills in Pre College Mathematics

## Try with Hints

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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