Set Theory Model Questions Set 2 Practice Questions Answers Test with Solutions & More Shortcuts
Set Theory PRACTICE TEST [2 - EXERCISES]
Set Theory Model Questions Set 1
Set Theory Model Questions Set 2
Question : 21
Consider the following for the next three (03) items : In a certain town of population size 1,00,000 three types of newspapers (I, II and III) are available. The percentages of the people in the town who read these papers are as follows :
Newspaper | Proportion of readers |
I | 10 % |
II | 30 % |
III | 5 % |
Both I and II | 8 % |
Both II and III | 4 % |
Both I and III | 2 % |
All the three (I, II and III) | 1 % |
a) 66, 000
b) 64, 000
c) 62, 000
d) 68, 000
Answer »Answer: (d)
Number of people who do not read any of these newspaper = total population – number of people who read atleast one of these newspapers.
number of people who read atleast one of these newspapers = 1% + 1% + 3% + 1% + 7% + 19% = 32% of total population = 32000
required number of people = 100000 – 32000 = 68000
Question : 22
If A = {x : $x^2$ – 6x + 8 = 0} and B = {x : $2x^2$ + 3x – 2 = 0} Then, which one of the following is correct?
a) Neither A ⊆ B nor B ⊆ A
b) B ⊆ A
c) A ⊆ B
d) A = B
Answer »Answer: (a)
Given, A ≡ $x^2$ – 6x + 8 = 0
⇒ (x – 4) (x – 2) = 0
⇒ x = 4, 2
and B ≡ $2x^2$ + 3x – 2 = 0
⇒ (2x – 1) (x + 2) = 0
⇒ x = $1/2$ , –2
Hence, neither A ⊆ B nor B ⊆ A.
Question : 23
Which one of the following is correct?
a) Φ ε {{Φ}, {{Φ}}}
b) {Φ} ε {{Φ}, {{Φ}}}
c) {Φ} ⊂ {{Φ}, {{Φ}}}
d) Φ = {{Φ}, {{Φ}}}
Answer »Answer: (b)
Here, {Φ} is an element of {Φ} ε {{Φ}, {{Φ}}}.
Question : 24
Which one of the following is a correct statement?
a) {x : x + 5 = 5} = 0
b) {x : x + 5 = 5} = {0}
c) {x : x + 5 = 5} = Φ
d) {x : x + 5 = 5} = {Φ}
Answer »Answer: (b)
Solving the given equation for x, we have
x + 5 = 5 ⇒ x = 5 – 5 = 0
Therefore, in the given set we have only one element i.e. 0. Element Φ is a null set i.e. no elements in the set.
Hence, option (b) is the correct answer.
Question : 25
If A = {x : x is an even natural number},
B = {x : x is a natural number and multiple of 5} and
C = {x : x is a natural number and multiple of 10},
then what is the value of A ∩ (B ∪ C)?
a) {2, 4, 6, ...}
b) {5, 10, 15, 20, ...}
c) {10, 20, 30, ...}
d) {20, 40, 60, ...}
Answer »Answer: (c)
We know that
A ∩ (B ∪ C) = {A ∩ B) ∪ (A ∩ C)
Example:
A = Set of an even natural number
A = {2, 4, 6, 8, 10, 12, ...}
B = Set of natural number and multiples of 5.
B = {5, 10, 15, 20, 25, ...}
C = Set of natural number and multiple of 10.
C = {10, 20, 30, 40, 50, ...}
A ∩ B = {2, 4, 6, 8, 10, 12, ...} ∩ {5, 10, 15, 20, 25, ...} = {10, 20, 30, ...}
A ∩ C = {2, 4, 6, 8, 10, 12, ...} ∩ {10, 20, 30, 40, 50, ...} = {10, 20, 30, 40, ...}
A ∩ (B ∪ C) = (A ∩ B) ∪ (A ∩ C)
= {10, 20, 30, ...} ∪ {10, 20, 30, 40, ...}
= {10, 20, 30, 40, ...}
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Set Theory Model Questions Set 2 Online Quiz
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