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# 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.**

Here are a few solved examples which will definitely help you.

### 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

#### CORRECT ANSWER(A)

### 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 = 6^{4}

n(s) = 6^{4}

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%

#### CORRECT ANSWER (C)

### 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**

Therefore, 9 people like both tea and coffee.

#### CORRECT ANSWER (D)

### 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

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