GATE CSE

All subjects All subjects Operating Systems132 Operating Systems132 DBMS122 DBMS122 Computer Networks142 Computer Networks142 Algorithms128 Algorithms128 Programming & Data Structures195 Programming & Data Structures195 Theory of Computation122 Theory of Computation122 Compiler Design95 Compiler Design95 Computer Organization & Architecture131 Computer Organization & Architecture131 Digital Logic91 Digital Logic91 Discrete Mathematics133 Discrete Mathematics133 Engineering Mathematics139 Engineering Mathematics139 General Aptitude260 General Aptitude260

Coming soon

BookmarksSoon

My progressSoon

Home
Previous Year
GATE
CSE
Discrete Mathematics
Sets & Relations

Back

GATE CSE previous year questions · Discrete Mathematics

Sets & Relations

31 questions

PYQ Hub · Previous year questions, organised for practice.Every question lists its source.

Sets & Relations (Discrete Mathematics): GATE CSE PYQs | PYQ Hub

Programming & Data Structures195

Theory of Computation122

Compiler Design95

Computer Organization & Architecture131

Digital Logic91

Discrete Mathematics133

Engineering Mathematics139

General Aptitude260

Home
Previous Year
GATE
CSE
Discrete Mathematics
Sets & Relations

Back

GATE CSE previous year questions · Discrete Mathematics

Sets & Relations

31 questions

Filters & sort

Sort

Filters

Year

2026 2025 2024 2023 2021 2020 2019 2018 2017

GATE CSE 2026 | Set 2 | Question 26

Sets & Relations

MSQ1 mark

Let

R

be a binary relation on the set

\{1, 2, \ldots, 10\}

, where

(x, y) \in R

if the product of

x

and

y

is square of an integer. Which of the following properties is/are satisfied by

R

One or more correct

Source: GATE CSE 2026 Set 2 (CS2), IIT Guwahati. Official question paper.

GATE CSE 2025 | Set 1 | Question 17

Sets & Relations

MCQ1 mark

g(.)

is a function from

A

B

f(.)

is a function from

B

C

, and their composition defined as

f(g(.))

is a mapping from

A

C

. If

f(.)

and

f(g(.))

are onto (surjective) functions, which ONE of the following is TRUE about the function

g(.)

Single correct

Source: GATE CSE 2025 Set 1 (CS1), IIT Roorkee. Official question paper.

GATE CSE 2025 | Set 2 | Question 42

Sets & Relations

MSQ2 marks

Let

\mathcal{F}

be the set of all functions from

\{1, \ldots, n\}

\{0, 1\}

. Define the binary relation

\preccurlyeq

\mathcal{F}

as follows:

\forall f, g \in \mathcal{F},\ f \preccurlyeq g \text{ if and only if } \forall x \in \{1, \ldots, n\},\ f(x) \le g(x), \text{ where } 0 \le 1.

Which of the following statement(s) is/are TRUE?

One or more correct

Source: GATE CSE 2025 Set 2 (CS2), IIT Roorkee. Official question paper.

GATE CSE 2024 | Set 1 | Question 32

Sets & Relations

NAT1 mark

Let

A

and

B

be non-empty finite sets such that there exist one-to-one and onto functions (i) from

A

B

and (ii) from

A \times A

A \cup B

. The number of possible values of

|A|

is __________

Numerical answer

Your answer

Source: GATE CSE 2024 Set 1 (CS1), IISc Bengaluru. Official question paper.

GATE CSE 2024 | Set 2 | Question 34

Sets & Relations

NAT1 mark

Let

P

be the partial order defined on the set

\{1,2,3,4\}

as follows

P = \{(x, x) \mid x \in \{1,2,3,4\}\} \cup \{(1,2), (3,2), (3,4)\}

The number of total orders on

\{1,2,3,4\}

that contain

P

is __________

Numerical answer

Your answer

Source: GATE CSE 2024 Set 2 (CS2), IISc Bengaluru. Official question paper.

GATE CSE 2023 | Question 49

Sets & Relations

MSQ2 marks

Let

f : A \to B

be an onto (or surjective) function, where

A

and

B

are nonempty sets. Define an equivalence relation

\sim

on the set

A

a_1 \sim a_2 \text{ if } f(a_1) = f(a_2),

where

a_1, a_2 \in A

. Let

\mathcal{E} = \{[x] : x \in A\}

be the set of all the equivalence classes under

\sim

. Define a new mapping

F : \mathcal{E} \to B

F([x]) = f(x), \text{ for all the equivalence classes } [x] \text{ in } \mathcal{E}.

Which of the following statements is/are TRUE?

One or more correct

Answer key coming soon

Source: GATE CSE 2023, IIT Kanpur. Official question paper.

GATE CSE 2021 | Set 1 | Question 43

Sets & Relations

MSQ2 marks

A relation R is said to be *circular* if

a\mathbf{R}b

and

b\mathbf{R}c

together imply

c\mathbf{R}a

. Which of the following options is/are correct?

One or more correct

Answer key coming soon

Source: GATE CSE 2021 Set 1 (CS1), IIT Bombay. Official question paper.

GATE CSE 2021 | Set 2 | Question 11

Sets & Relations

MSQ1 mark

Consider the following sets, where

n \ge 2

S_1

: Set of all

n \times n

matrices with entries from the set

\{a, b, c\}

S_2

: Set of all functions from the set

\{0, 1, 2, \ldots, n^2 - 1\}

to the set

\{0, 1, 2\}

Which of the following choice(s) is/are correct?

One or more correct

Answer key coming soon

Source: GATE CSE 2021 Set 2 (CS2), IIT Bombay. Official question paper.

GATE CSE 2021 | Set 2 | Question 50

Combinatorics·Sets & Relations

NAT2 marks

Let

S

be a set consisting of 10 elements. The number of tuples of the form

(A, B)

such that

A

and

B

are subsets of

S

, and

A \subseteq B

is ________.

Numerical answer

Your answer

Answer key coming soon

Source: GATE CSE 2021 Set 2 (CS2), IIT Bombay. Official question paper.

GATE CSE 2020 | Question 17

Sets & Relations·Probability & Statistics

NAT1 mark

Let

\mathcal{R}

be the set of all binary relations on the set

\{1,2,3\}

. Suppose a relation is chosen from

\mathcal{R}

at random. The probability that the chosen relation is reflexive (round off to 3 decimal places) is _______.

Numerical answer

Your answer

Answer key coming soon

Source: GATE CSE 2020, IIT Delhi. Official question paper.

GATE CSE 2019 | Question 5

Combinatorics·Sets & Relations

MCQ1 mark

Let

U = \{1, 2, \ldots, n\}

. Let

A = \{(x, X) \mid x \in X, X \subseteq U\}

. Consider the following two statements on

|A|

. I.

|A| = n2^{n-1}

II.

|A| = \sum_{k=1}^{n} k\binom{n}{k}

Which of the above statements is/are TRUE?

Single correct

Source: GATE CSE 2019, IIT Madras. Official question paper and answer key.

GATE CSE 2019 | Question 10

Group Theory·Sets & Relations

MCQ1 mark

Let

G

be an arbitrary group. Consider the following relations on

G

R_1

\forall a, b \in G

a R_1 b

if and only if

\exists g \in G

such that

a = g^{-1}bg

R_2

\forall a, b \in G

a R_2 b

if and only if

a = b^{-1}

Which of the above is/are equivalence relation/relations?

Single correct

Source: GATE CSE 2019, IIT Madras. Official question paper and answer key.

GATE CSE 2019 | Question 34

Decidability·Sets & Relations

MCQ2 marks

Consider the following sets: S1. Set of all recursively enumerable languages over the alphabet

\{0, 1\}

S2. Set of all syntactically valid C programs S3. Set of all languages over the alphabet

\{0, 1\}

S4. Set of all non-regular languages over the alphabet

\{0, 1\}

Which of the above sets are uncountable?

Single correct

Source: GATE CSE 2019, IIT Madras. Official question paper and answer key.

Let N be the set of natural numbers. Consider the following sets. P: Set of Rational numbers (positive and negative) Q: Set of functions from {0, 1} to N R: Set of functions from N to {0, 1} S: Set of finite subsets of N. Which of the sets above are countable?

Single correct

Source: GATE CSE 2018, IIT Guwahati. Official question paper and answer key.

GATE CSE 2017 | Set 2 | Question 21

Sets & Relations

NAT1 mark

Consider the set

X = \{a, b, c, d, e\}

under the partial ordering

R = \{(a,a), (a,b), (a,c), (a,d), (a,e), (b,b), (b,c), (b,e), (c,c), (c,e), (d,d), (d,e), (e,e)\}.

The Hasse diagram of the partial order

(X, R)

is shown below. The minimum number of ordered pairs that need to be added to

R

to make

(X, R)

a lattice is ________.

Figure for GATE CSE 2017 | Set 2 | Question 21

Numerical answer

Your answer

Answer key coming soon

Source: GATE CSE 2017 Set 2, IIT Roorkee. Official question paper.

GATE CSE 2016 | Set 1 | Question 28

Sets & Relations

NAT2 marks

A function

f: \mathbb{N}^+ \to \mathbb{N}^+

, defined on the set of positive integers

\mathbb{N}^+

, satisfies the following properties:

f(n) = f(n/2) \quad \text{if } n \text{ is even}

f(n) = f(n + 5) \quad \text{if } n \text{ is odd}

Let

R = \{i \mid \exists j : f(j) = i\}

be the set of distinct values that

f

takes. The maximum possible size of

R

is ________.

Numerical answer

Your answer

Answer key coming soon

Source: GATE CSE 2016 Set 1, IISc Bengaluru. Official question paper.

GATE CSE 2016 | Set 2 | Question 26

Sets & Relations

MCQ2 marks

A binary relation

R

\mathbb{N} \times \mathbb{N}

is defined as follows:

(a, b)R(c, d)

a \le c

b \le d

. Consider the following propositions: P:

R

is reflexive Q:

R

is transitive Which one of the following statements is TRUE?

Single correct

Answer key coming soon

Source: GATE CSE 2016 Set 2, IISc Bengaluru. Official question paper.

GATE CSE 2015 | Set 1 | Question 11

Calculus·Sets & Relations

MCQ1 mark

g(x) = 1 - x

and

h(x) = \frac{x}{x - 1}

, then

\frac{g(h(x))}{h(g(x))}

is:

Single correct

Source: GATE CSE 2015 Set 1, IIT Kanpur. Official question paper and answer key.

GATE CSE 2015 | Set 1 | Question 20

Sets & Relations

MCQ1 mark

For a set

A

, the power set of

A

is denoted by

2^A

. If

A = \{5, \{6\}, \{7\}\}

, which of the following options are TRUE? I.

\emptyset \in 2^A

II.

\emptyset \subseteq 2^A

III.

\{5, \{6\}\} \in 2^A

IV.

\{5, \{6\}\} \subseteq 2^A

Single correct

Source: GATE CSE 2015 Set 1, IIT Kanpur. Official question paper and answer key.

GATE CSE 2015 | Set 1 | Question 42

Sets & Relations

MCQ2 marks

Suppose

\mathcal{L} = \{p, q, r, s, t\}

is a lattice represented by the following Hasse diagram: For any

x, y \in \mathcal{L}

, not necessarily distinct,

x \lor y

and

x \land y

are join and meet of

x, y

, respectively. Let

\mathcal{L}^3 = \{(x, y, z): x, y, z \in \mathcal{L}\}

be the set of all ordered triplets of the elements of

\mathcal{L}

. Let

p_r

be the probability that an element

(x, y, z) \in \mathcal{L}^3

chosen equiprobably satisfies

x \lor (y \land z) = (x \lor y) \land (x \lor z)

. Then

Figure for GATE CSE 2015 | Set 1 | Question 42

Single correct

Source: GATE CSE 2015 Set 1, IIT Kanpur. Official question paper and answer key.

Use ← → to move

Questions

31 total

Correct Wrong Answer seen

1 2

Sort

Filters

Year

Set

Set

Marks

Marks

Question type

Question type