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Test: Set Theory- 2


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10 Questions MCQ Test CSAT Preparation for UPSC CSE | Test: Set Theory- 2

Test: Set Theory- 2 for CAT 2022 is part of CSAT Preparation for UPSC CSE preparation. The Test: Set Theory- 2 questions and answers have been prepared according to the CAT exam syllabus.The Test: Set Theory- 2 MCQs are made for CAT 2022 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for Test: Set Theory- 2 below.
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Test: Set Theory- 2 - Question 1

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

Test: Set Theory- 2 - Question 2

 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 for Test: Set Theory- 2 - 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

Test: Set Theory- 2 - Question 3

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 ?

Test: Set Theory- 2 - Question 4

Order of the power set of a set of order n is

Test: Set Theory- 2 - Question 5

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

Test: Set Theory- 2 - Question 6

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 for Test: Set Theory- 2 - 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

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

The set of all Equivalence classes of a set A of cardinality C

Test: Set Theory- 2 - Question 9

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

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 for Test: Set Theory- 2 - 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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