# Set Theory Model Questions Set 1 Practice Questions Answers Test With Solutions & More Shortcuts

#### SET THEORY PRACTICE TEST [2 - EXERCISES]

Question : 1

Which one of the following is not correct in respect of the sets A and B?

a) If A ⊆ B, then B ∩ A = A

b) If A ⊆ B, then A ∩ (A – B) = Φ

c) If A ⊆ B, then B ∪ A = B

d) If A ∩ B = Φ, then either A = Φ or B = Φ

If A ∩ B = Φ, then it is not necessary that either A = f or B = f

Question : 2

In a school there are 30 teachers who teach Mathematics or Physics. Of these teachers, 20 teach Mathematics and 15 teach Physics, 5 teach both Mathematics and Physics. The number of teachers teaching only Mathematics is

a) 15

b) 10

c) 5

d) 20

Total number of teachers = 30.

Number of teachers who teaches only Math

= 20 – 5 = 15.

Question : 3

Consider the following for the next 04 (four) items that follow : In an examination of Class XII, 55% students passed in Biology, 62% passed in Physics, 60% passed in Chemistry, 25% passed in Physics and Biology, 30% passed in Physics and Chemistry, 28% passed in Biology and Chemistry. Only 2% failed in all the subjects.If the number of students is 360, then how many passed in at least two subjects?

a) 265

b) 263

c) 270

d) 260

Passed in at least two subject

= \${25 - x + 30 - x + 28 - x + x}/{100}\$ × 360

= \${83 - 2x}/{100}\$ × 360 = 270

Question : 4

Out of 105 students taking an examination English and Mathematics, 80 students pass in English, 75 students pass in Mathematics 10 students fail in both the subjects. How many students fail in only one subject?

a) 35

b) 30

c) 26

d) 45

Number of students failing in Mathematics

= 105 – 75 = 30

Number of students failing in English

= 105 – 80 = 25

∴ Number of students failing in 1 subject

= (25 + 30) – 10 = 45

Question : 5

In a gathering of 100 people, 70 of them can speak Hindi, 60 can speak English and 30 can speak French Further, 30 of them can speak both Hindi and English. 20 can speak both Hindi and French. If x is the number of people who can speak both English and French, then which one of the following is correct? (Assume that everyone can speak at least one of the three languages)

a) x = 9

b) 0 ≤ x < 8

c) 9 < x ≤ 30

d) x = 8

Let n(A) be no. of people who speak Hindi

⇒ n(A) = 70

Let n(B) be no. of people who speak English

⇒ n(B) = 60

Let n(C) be no. of people who speak French

⇒ n(C) = 30

Given n (A ∪ B ∪ C) = 100

n(A ∩ B) = 30, n(A ∪ C) = 20

n (B ∩ C) = x, n(A ∩ B ∩ C) = 1

We know that

n(A ∪ B ∪ C) = n(A) + n(B) + n (C) - n(A ∩ B)

- n (B ∩ C) - n(C ∩ A) - n(A ∩ B ∩ C)

100 = 70 + 60 + 30 – 30 – x – 20 – 1

100 = 109 – x

⇒ x = 109 – 100

⇒ x = 9

∴ Option (a) is correct.

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