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CAT Exam  >  CAT Test  >  Quantitative Aptitude (Quant)  >  Test: Set Theory- 2 - CAT MCQ

Set Theory- 2 - Free MCQ Practice Test with solutions, CAT Quant Aptitude


MCQ Practice Test & Solutions: Test: Set Theory- 2 (10 Questions)

You can prepare effectively for CAT Quantitative Aptitude (Quant) with this dedicated MCQ Practice Test (available with solutions) on the important topic of "Test: Set Theory- 2". These 10 questions have been designed by the experts with the latest curriculum of CAT 2026, to help you master the concept.

Test Highlights:

  • - Format: Multiple Choice Questions (MCQ)
  • - Duration: 10 minutes
  • - Number of Questions: 10

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Test: Set Theory- 2 - Question 1
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The number of elements in the power set of the set {{a, b}, c} is

Detailed Solution: Question 1

We can simply solve this problem by using the following mathematical process.

A power set is defined as the set or group of all subsets for any given set, including the empty set.  A set that has 'n' elements has 2n subsets in all.

The power set is denoted by the notation P(S) and the number of elements of the power set is given by 2n.

In the given set, the number of elements is 2

Therefore, in the power set, the number of elements will be

Hence, The number of elements in the power set of the set {{a,b},c} is 4.

Test: Set Theory- 2 - Question 2
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 If R = ((1, 1), (3, 1), (2, 3), (4, 2)), then which of the following represents R2, where R2 is R composite R?

Detailed Solution: Question 2

The correct answer is D as
 R = ((1, 1), (3, 1), (2, 3), (4, 2))
RoR=R2=((1, 1), (3, 1), (2, 3), (4, 2))((1, 1), (3, 1), (2, 3), (4, 2))
     =((1, 1), (3, 1), (2, 1), (4, 3))
take the first set (1,1) then take the second element of this subset check in the other set R is there any starting with 1 if yes then take its second element and make a subset in R2 similarly check for all.
like (4,2) (2,3)=(4,3)in R2

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Test: Set Theory- 2 - Question 3
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In a room containing 28 people, there are 18 people who speak English, 15 people who speak Hindi and 22 people who speak Kannada, 9 persons speak both English and Hindi, 11 persons speak both Hindi and Kannada where as 13 persosn speak both Kannada and English. How many people speak all the three languages ?

Detailed Solution: Question 3

Let X was the people who speaks all three languages.
Total number of people = (Hindi + English + Kannad) - (Hindi and English + Hindi and Kannad + Kannad and English) + X

28 = (15 + 22 + 18) - (9 + 11 + 13) +X

X = 28 - 55 + 33

X = 6.

Test: Set Theory- 2 - Question 4
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Order of the power set of a set of order n is

Test: Set Theory- 2 - Question 5
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If f : R ---->R defined by f(x) = x2 + 1, then values of f -1 (17) and  f -1(-3) are respectively

Detailed Solution: Question 5



Test: Set Theory- 2 - Question 6
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In a beauty contest, half the number of experts voted for Mr. A and two thirds voted for Mr. B. 10 voted for both and 6 did not vote for either. How many experts were there in all ?

Detailed Solution: Question 6

The correct answer is C as
Let,the number of voters (experts) be denoted as x
A/Q
 X/2+2x/3-10+6=x
7x/6-4=x
7x-24=6x
x=24
 

Test: Set Theory- 2 - Question 7
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Let n(A) denotes the number of elements in set A. If n(A) =p and n(B) = q, then how many ordered pairs (a, b) are there with a ∈ A and b ∈ B ?

Test: Set Theory- 2 - Question 8
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The set of all Equivalence classes of a set A of cardinality C

Test: Set Theory- 2 - Question 9
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Let Z denote the set of all integers.
Define f : Z —> Z by
f(x) = {x / 2 (x is even)
            0     (x is odd)
then f is

Test: Set Theory- 2 - Question 10
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Let R be a relation "(x -y) is divisible by m", where x, y, m are integers and m > 1, then R is

Detailed Solution: Question 10

a) Since x - x = 0, m
=> x - x is divisible by m
(x,x) ∈ R
=> R is reflexive
b) Let (x,y) ∈ R
=> x - y = mq for some q ∈ I
=> y - x = m(-q)
y - x is divisible by m
(y,x) ∈ R
=> R is symmetric.
c) Let (x,y) and (y,z) ∈ R
=> x - y is divisible by m and y - z is divisible by m
=> x - y = mq and y - z = mq' for some q, q' ∈ I
=>(x-y)+(y-z) = m(q+q')
=> x - z = m(q + q'), q + q' ∈ I
(x,z) ∈ R
=> R is transitive.
Hence the relation is equivalence relation.

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About this CAT Practice Test

This test contains 10 MCQs on Set Theory- 2 with detailed solutions for each question. It is part of the Quantitative Aptitude (Quant) course on EduRev, designed to align with the current CAT syllabus. Each solution explains not just the correct answer but also gives you an understanding of the topic — not just to attempt the question but also help you prepare for the exam with practice.

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