Sets, Relations, Functions, Partial Orders and Lattices: GATE CS previous year questions (Engineering Mathematics)

GATE CS 2026 Set 2MSQ1 markEasy (estimate)
GATE CS 2026 Set 2, Q.26
Let $R$ be a binary relation on the set ${1, 2, \dots, 10}$ , where $(x, y) \in R$ if the product of $x$ and $y$ is square of an integer. Which of the following properties is/a...
Sets, Relations, Functions, Partial Orders and Lattices
GATE CS 2025 Set 1MCQ1 markEasy (estimate)
GATE CS 2025 Set 1, Q.17
$g (.)$ is a function from $A$ to $B$ , $f (.)$ is a function from $B$ to $C$ , and their composition defined as $f (g (.))$ is a mapping from $A$ to $C$ . If $f (.)$ and $f (g (.))$ are...
Sets, Relations, Functions, Partial Orders and Lattices
GATE CS 2025 Set 2MSQ2 marksEasy (estimate)
GATE CS 2025 Set 2, Q.42
Let $F$ be the set of all functions from ${1, \dots, n}$ to ${0, 1}$ . Define the binary relation $≼$ on $F$ as follows…
Sets, Relations, Functions, Partial Orders and Lattices
GATE CS 2024 Set 1NAT1 markMedium (estimate)
GATE CS 2024 Set 1, Q.32
Let $A$ and $B$ be non-empty finite sets such that there exist one-to-one and onto functions (i) from $A$ to $B$ and (ii) from $A \times A$ to $A \cup B$ . The number of possible...
Sets, Relations, Functions, Partial Orders and Lattices
GATE CS 2024 Set 2MCQ1 markEasy (estimate)
GATE CS 2024 Set 2, Q.3
In an engineering college of 10,000 students, 1,500 like neither their core branches nor other branches. The number of students who like their core branches is $1/ 4^{th}$ ...
Quantitative Aptitude · Sets, Relations, Functions, Partial Orders and Lattices
GATE CS 2024 Set 2NAT1 markEasy (estimate)
GATE CS 2024 Set 2, Q.34
Let $P$ be the partial order defined on the set ${1, 2, 3, 4}$ as follows $P = {(x, x) ∣ x \in {1, 2, 3, 4}} \cup {(1, 2), (3, 2), (3, 4)}$ The number of total orders on…
Sets, Relations, Functions, Partial Orders and Lattices · Combinatorics, Counting, Recurrence Relations and Generating Functions
GATE CS 2023MSQ2 marksMedium (estimate)
GATE CS 2023, Q.49
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 $A$ as…
Sets, Relations, Functions, Partial Orders and Lattices
GATE CS 2023MSQ2 marksMedium (estimate)
GATE CS 2023, Q.51
Let $X$ be a set and $2^{X}$ denote the powerset of $X$ . Define a binary operation $Δ$ on $2^{X}$ as follows: $A Δ B = (A - B) \cup (B - A) .$ Let $H = (2^{X}, Δ)$ . Wh...
Monoids and Groups · Sets, Relations, Functions, Partial Orders and Lattices
GATE CS 2021 Set 1MSQ2 marksMedium (estimate)
GATE CS 2021 Set 1, Q.53 (CS Q.43)
A relation $R$ is said to be circular if $a R b$ and $b R c$ together imply $c R a$ . Which of the following options is/are correct?
Sets, Relations, Functions, Partial Orders and Lattices
GATE CS 2021 Set 2MSQ1 markEasy (estimate)
GATE CS 2021 Set 2, Q.21 (CS Q.11)
Consider the following sets, where $n \geq 2$ : $S_{1}$ : Set of all $n \times n$ matrices with entries from the set ${a, b, c}$ $S_{2}$ : Set of all functions from the set…
Sets, Relations, Functions, Partial Orders and Lattices
GATE CS 2020NAT1 markEasy (estimate)
GATE CS 2020, Q.27 (CS Q.17)
Let $R$ be the set of all binary relations on the set ${1, 2, 3}$ . Suppose a relation is chosen from $R$ at random. The probability that the chosen relation is reflexive (roun...
Sets, Relations, Functions, Partial Orders and Lattices · Probability and Statistics
GATE CS 2019NAT2 marksEasy (estimate)
GATE CS 2019, Q.64 (CS Q.54)
In an RSA cryptosystem, the value of the public modulus parameter $n$ is 3007. If it is also known that $ϕ (n) = 2880$ , where $ϕ ()$ denotes Euler's Totient Function, then t...
Application Layer: DNS, HTTP, SMTP, FTP · Sets, Relations, Functions, Partial Orders and Lattices
GATE CS 2017 Set 2NAT1 markMedium (estimate)
GATE CS 2017 Set 2, Q.21 (CS Q.21)
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 Has...
Sets, Relations, Functions, Partial Orders and Lattices
GATE CS 2016 Set 1NAT2 marksHard (estimate)
GATE CS 2016 Set 1, Q.38 (CS Q.28)
A function $f : N^{+} \to N^{+}$ , defined on the set of positive integers $N^{+}$ , satisfies the following properties…
Sets, Relations, Functions, Partial Orders and Lattices
GATE CS 2016 Set 2MCQ2 marksMedium (estimate)
GATE CS 2016 Set 2, Q.36 (CS Q.26)
A binary relation $R$ on $N \times N$ is defined as follows: $(a, b) R (c, d)$ if $a \leq c$ or $b \leq d$ . Consider the following propositions: $P$ : $R$ is reflex...
Sets, Relations, Functions, Partial Orders and Lattices
GATE CS 2015 Set 1MCQ1 markMedium (estimate)
GATE CS 2015 Set 1, Q.15 (CS Q.5)
If $g (x) = 1 - x$ and $h (x) = \frac{x}{x - 1}$ , then $\frac{g ( h ( x ))}{h ( g ( x ))}$ is:
Sets, Relations, Functions, Partial Orders and Lattices
GATE CS 2015 Set 1MCQ1 markMedium (estimate)
GATE CS 2015 Set 1, Q.26 (CS Q.16)
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.…
Sets, Relations, Functions, Partial Orders and Lattices
GATE CS 2015 Set 1MCQ2 marksHard (estimate)
GATE CS 2015 Set 1, Q.44 (CS Q.34)
Suppose $L = {p, q, r, s, t}$ is a lattice represented by the following Hasse diagram: For any $x, y \in L$ , not necessarily distinct, $x \lor y$ and $x \land y$ are join and...
Sets, Relations, Functions, Partial Orders and Lattices
GATE CS 2015 Set 2MCQ1 markEasy (estimate)
GATE CS 2015 Set 2, Q.26 (CS Q.16)
Let $R$ be the relation on the set of positive integers such that $a R b$ if and only if $a$ and $b$ are distinct and have a common divisor other than 1. Which one of the followin...
Sets, Relations, Functions, Partial Orders and Lattices
GATE CS 2015 Set 2NAT1 markEasy (estimate)
GATE CS 2015 Set 2, Q.28 (CS Q.18)
The cardinality of the power set of ${0, 1, 2, \dots, 10}$ is _____.
Sets, Relations, Functions, Partial Orders and Lattices
GATE CS 2015 Set 3MCQ1 markEasy (estimate)
GATE CS 2015 Set 3, Q.33 (CS Q.23)
Suppose $U$ is the power set of the set $S = {1, 2, 3, 4, 5, 6}$ . For any $T \in U$ , let $∣ T ∣$ denote the number of elements in $T$ and $T^{'}$ denote the complement of $T$ . For...
Sets, Relations, Functions, Partial Orders and Lattices
GATE CS 2015 Set 3MCQ2 marksMedium (estimate)
GATE CS 2015 Set 3, Q.51 (CS Q.41)
Let $R$ be a relation on the set of ordered pairs of positive integers such that $((p, q), (r, s)) \in R$ if and only if $p - s = q - r$ . Which one of the following is true abou...
Sets, Relations, Functions, Partial Orders and Lattices
GATE CS 2014 Set 1NAT2 marksEasy (estimate)
GATE CS 2014 Set 1, Q.60 (CS Q.50)
Let $S$ denote the set of all functions $f : {0, 1}^{4} \to {0, 1}$ . Denote by $N$ the number of functions from $S$ to the set ${0, 1}$ . The value of $lo g_{2} lo g_{2} N$ is ______.
Sets, Relations, Functions, Partial Orders and Lattices
GATE CS 2014 Set 2MCQ2 marksHard (estimate)
GATE CS 2014 Set 2, Q.60 (CS Q.50)
Consider the following relation on subsets of the set $S$ of integers between 1 and 2014. For two distinct subsets $U$ and $V$ of $S$ we say $U < V$ if the minimum element in th...
Sets, Relations, Functions, Partial Orders and Lattices
GATE CS 2014 Set 3MCQ1 markMedium (estimate)
GATE CS 2014 Set 3, Q.12 (CS Q.2)
Let $X$ and $Y$ be finite sets and $f : X \to Y$ be a function. Which one of the following statements is TRUE?
Sets, Relations, Functions, Partial Orders and Lattices
GATE CS 2014 Set 3MCQ2 marksMedium (estimate)
GATE CS 2014 Set 3, Q.59 (CS Q.49)
Consider the set of all functions $f : {0, 1, \dots, 2014} \to {0, 1, \dots, 2014}$ such that $f (f (i)) = i$ , for all $0 \leq i \leq 2014$ . Consider the following statements: P....
Sets, Relations, Functions, Partial Orders and Lattices

Questions

Other topics of Engineering Mathematics