# How To Solve Set Theory Questions Quickly

## HOW TO SOLVE – SET THEORY

DEFINITION

Set Theory is a branch of Mathematics that deals with the properties of well- defined collections of an object.

In other words, its natural habit for all of us to classify similar things into groups. These groups are known as Set.

This page is basically to help students and let them solve the questions quickly. We are going to provide you the best ways to solve the questions quickly.

The best way to solve the question is by practicing them and before practicing we need to see the Solved Examples.

### Question 1

In a class of 100 students, 35 like science and 45 like math. 10 like both. How many like either of them and how many like neither?

OPTIONS
a) 30

b) 24

c)31

d)18

Explanations

Total number of students, n(µ) = 100

Number of science students, n(S) = 35

Number of math students, n(M) = 45

Number of students who like both, n(M∩S) = 10

Number of students who like either of them,

n(MᴜS) = n(M) + n(S) – n(M∩S)

→ 45+35-10 = 70

Number of students who like neither = n(µ) – n(MᴜS) = 100 – 70 = 30

### Question 2

Four dice are thrown simultaneously. Find the probability that all of them show the same face.

OPTIONS

a) $\frac{1}{216} \$

b) $\frac{1}{316} \$

c) $\frac{4}{216} \$

d) $\frac{1}{36} \$

Explanation

Throwing 4 dice simultaneously show
6×6×6×6 = 64
n(s) = 64

Let x, be the event of all dice showing the same face.
x = { (1,1,1,1), (2,2,2,2), (3,3,3,3), (4,4,4,4), (5,5,5,5), (6,6,6,6) }

n(x) =6

hence required probability

$\frac{n (x)}{n(s)} \$$\frac{6}{6^4} \$

$\frac{1}{216} \$

### Question 3

In a class there are 60% of girls of which 25% poor. What is the probability that a poor girl is selected is leader?

OPTIONS

a) 31 %

b) 23%

c) 15%

d) 17%

Explanation

Assume total students in the class = 100

Then Girls = 60% (100) = 60

Poor girls = 25% (60) = 15

So probability that a poor girls is selected leader = $\frac{Poor girls}{total student} \$ = $\frac{15}{100} \$ = 15%

### Question 4

In a group of 60 people, 27 like tea and 42 like coffee and each person likes at least one of the two drinks. How many like both coffee and tea?

OPTIONS
a) 12
b) 3
c) 8
d) 9

Explanation
Let A = Set of people who like tea
B = Set of people who like coffee
Given,
(A ∪B) = 60
n(A) = 27
n(B) = 42
n(A) + n(B) – n(A ∪ B)
= 27 + 42 – 60
= 69 – 60 = 9
= 9

Therefore, 9 people like both tea and coffee.

### Question 5

Let A and B be two finite sets such that n(A) = 24, n(B) = 37 and n(A ∪ B) = 46, find n(A ∩ B).

OPTIONS

a)12

b) 15

c) 8

d) 4

Explanation

Using the formula n(A ∪ B) = n(A) + n(B) – n(A ∩ B).

then n(A ∩ B) = n(A) + n(B) – n(A ∪ B)
= 24 +37 – 46

= 61- 46
= 15