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This mock test of Test: Set Theory- 2 for CAT helps you for every CAT entrance exam.
This contains 10 Multiple Choice Questions for CAT Test: Set Theory- 2 (mcq) to study with solutions a complete question bank.
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QUESTION: 1

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

Solution:

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?

Solution:

The correct answer is D as

R = ((1, 1), (3, 1), (2, 3), (4, 2))

RoR=R^{2}=((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 R^{2} similarly check for all.

like (4,2) (2,3)=(4,3)in R^{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 ?

Solution:

QUESTION: 4

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

Solution:

QUESTION: 5

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

Solution:

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 ?

Solution:

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

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 ?

Solution:

QUESTION: 8

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

Solution:

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

Solution:

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

Solution:

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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