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Previous GATE
Featured
Highest voted questions in Discrete Mathematics
54
votes
6
answers
61
GATE CSE 1997 | Question: 6.3
The number of equivalence relations of the set $\{1,2,3,4\}$ is $15$ $16$ $24$ $4$
Kathleen
asked
in
Set Theory & Algebra
Sep 29, 2014
by
Kathleen
21.2k
views
gate1997
set-theory&algebra
relations
normal
54
votes
6
answers
62
GATE CSE 2006 | Question: 26
Which one of the first order predicate calculus statements given below correctly expresses the following English statement? Tigers and lions attack if they are hungry or threatened. ...
Rucha Shelke
asked
in
Mathematical Logic
Sep 18, 2014
by
Rucha Shelke
9.1k
views
gatecse-2006
mathematical-logic
normal
first-order-logic
54
votes
7
answers
63
GATE CSE 2009 | Question: 3
Which one of the following is TRUE for any simple connected undirected graph with more than $2$ vertices? No two vertices have the same degree. At least two vertices have the same degree. At least three vertices have the same degree. All vertices have the same degree.
gatecse
asked
in
Graph Theory
Sep 15, 2014
by
gatecse
11.3k
views
gatecse-2009
graph-theory
normal
degree-of-graph
53
votes
5
answers
64
GATE CSE 2014 Set 3 | Question: 1
Consider the following statements: P: Good mobile phones are not cheap Q: Cheap mobile phones are not good L: P implies Q M: Q implies P N: P is equivalent to Q Which one of the following about L, M, and N is CORRECT? Only L is TRUE. Only M is TRUE. Only N is TRUE. L, M and N are TRUE.
go_editor
asked
in
Mathematical Logic
Sep 28, 2014
by
go_editor
10.5k
views
gatecse-2014-set3
mathematical-logic
easy
propositional-logic
53
votes
5
answers
65
GATE CSE 2001 | Question: 2.2
Consider the following statements: $S_1:$ There exists infinite sets $A$, $B$, $C$ such that $A \cap (B \cup C)$ is finite. $S_2:$ There exists two irrational numbers $x$ and y such that $(x+y)$ ... $S_2$? Only $S_1$ is correct Only $S_2$ is correct Both $S_1$ and $S_2$ are correct None of $S_1$ and $S_2$ is correct
Kathleen
asked
in
Set Theory & Algebra
Sep 14, 2014
by
Kathleen
8.9k
views
gatecse-2001
set-theory&algebra
normal
set-theory
52
votes
6
answers
66
GATE CSE 2018 | Question: 27
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 above sets are countable? $Q$ and $S$ only $P$ and $S$ only $P$ and $R$ only $P, Q$ and $S$ only
gatecse
asked
in
Set Theory & Algebra
Feb 14, 2018
by
gatecse
21.8k
views
gatecse-2018
set-theory&algebra
countable-uncountable-set
normal
2-marks
52
votes
8
answers
67
GATE CSE 2013 | Question: 27
What is the logical translation of the following statement? "None of my friends are perfect." $∃x(F (x)∧ ¬P(x))$ $∃ x(¬ F (x)∧ P(x))$ $ ∃x(¬F (x)∧¬P(x))$ $ ¬∃ x(F (x)∧ P(x))$
Arjun
asked
in
Mathematical Logic
Sep 24, 2014
by
Arjun
14.0k
views
gatecse-2013
mathematical-logic
easy
first-order-logic
52
votes
6
answers
68
GATE CSE 2001 | Question: 2.15
How many undirected graphs (not necessarily connected) can be constructed out of a given set $V=\{v_1, v_2, \dots v_n\}$ of $n$ vertices? $\frac{n(n-1)} {2}$ $2^n$ $n!$ $2^\frac{n(n-1)} {2} $
Kathleen
asked
in
Graph Theory
Sep 14, 2014
by
Kathleen
14.0k
views
gatecse-2001
graph-theory
normal
counting
52
votes
2
answers
69
GATE CSE 1991 | Question: 16,a
Find the number of binary strings $w$ of length $2n$ with an equal number of $1's$ and $0's$ and the property that every prefix of $w$ has at least as many $0's$ as $1's.$
Kathleen
asked
in
Combinatory
Sep 12, 2014
by
Kathleen
6.4k
views
gate1991
combinatory
normal
descriptive
catalan-number
51
votes
3
answers
70
GATE CSE 2015 Set 3 | Question: 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 any $T, R \in U \text{ let } T \backslash R$ be the set ... $X \backslash Y = \phi)$ $\forall X \in U, \forall Y \in U, (X \backslash Y = Y' \backslash X')$
go_editor
asked
in
Set Theory & Algebra
Feb 14, 2015
by
go_editor
12.0k
views
gatecse-2015-set3
set-theory&algebra
set-theory
normal
51
votes
15
answers
71
GATE CSE 2015 Set 2 | Question: 40
The number of onto functions (surjective functions) from set $X = \{1, 2, 3, 4\}$ to set $Y=\{a,b,c\}$ is ______.
go_editor
asked
in
Set Theory & Algebra
Feb 12, 2015
by
go_editor
19.3k
views
gatecse-2015-set2
set-theory&algebra
functions
normal
numerical-answers
51
votes
12
answers
72
GATE CSE 2014 Set 1 | Question: 53
Which one of the following propositional logic formulas is TRUE when exactly two of $p,q$ and $r$ are TRUE? $(( p \leftrightarrow q) \wedge r) \vee (p \wedge q \wedge \sim r)$ $( \sim (p \leftrightarrow q) \wedge r)\vee (p \wedge q \wedge \sim r)$ ... $(\sim (p \leftrightarrow q) \wedge r) \wedge (p \wedge q \wedge \sim r) $
go_editor
asked
in
Mathematical Logic
Sep 28, 2014
by
go_editor
13.5k
views
gatecse-2014-set1
mathematical-logic
normal
propositional-logic
51
votes
5
answers
73
GATE CSE 2010 | Question: 1
Let $G=(V, E)$ be a graph. Define $\xi(G) = \sum\limits_d i_d*d$, where $i_d$ is the number of vertices of degree $d$ in $G.$ If $S$ and $T$ are two different trees with $\xi(S) = \xi(T)$, then $| S| = 2| T |$ $| S | = | T | - 1$ $| S| = | T | $ $| S | = | T| + 1$
gatecse
asked
in
Graph Theory
Sep 21, 2014
by
gatecse
11.4k
views
gatecse-2010
graph-theory
normal
degree-of-graph
51
votes
4
answers
74
GATE CSE 1991 | Question: 01,xv
The maximum number of possible edges in an undirected graph with $n$ vertices and $k$ components is ______.
Kathleen
asked
in
Graph Theory
Sep 12, 2014
by
Kathleen
11.5k
views
gate1991
graph-theory
graph-connectivity
normal
fill-in-the-blanks
50
votes
8
answers
75
GATE CSE 2016 Set 2 | Question: 26
A binary relation $R$ on $\mathbb{N} \times \mathbb{N}$ is defined as follows: $(a, b) R(c, d)$ if $a \leq c$ or $b \leq d$. Consider the following propositions: $P:$ $R$ is reflexive. $Q:$ $R$ is transitive. Which one of the following statements is TRUE? ... and $Q$ are true. $P$ is true and $Q$ is false. $P$ is false and $Q$ is true. Both $P$ and $Q$ are false.
Akash Kanase
asked
in
Set Theory & Algebra
Feb 12, 2016
by
Akash Kanase
14.6k
views
gatecse-2016-set2
set-theory&algebra
relations
normal
50
votes
9
answers
76
GATE IT 2005 | Question: 36
Let $P(x)$ and $Q(x)$ ...
Ishrat Jahan
asked
in
Mathematical Logic
Nov 3, 2014
by
Ishrat Jahan
14.7k
views
gateit-2005
mathematical-logic
first-order-logic
normal
50
votes
4
answers
77
GATE CSE 2005 | Question: 41
What is the first order predicate calculus statement equivalent to the following? "Every teacher is liked by some student" $∀(x)\left[\text{teacher}\left(x\right) → ∃(y) \left[\text{student}\left(y\right) → \text{likes}\left(y,x\right)\right]\right]$ ...
gatecse
asked
in
Mathematical Logic
Sep 21, 2014
by
gatecse
11.7k
views
gatecse-2005
mathematical-logic
easy
first-order-logic
49
votes
6
answers
78
GO Classes Weekly Quiz 5 | Propositional Logic | Question: 16
If $\text{F1, F2}$ and $\text{F3}$ are propositional formulae/expressions, over some set of propositional variables, such that $\mathrm{F} 1 \vee F 2 \rightarrow \mathrm{F} 3$ is a contradiction, then which of the following is/are ... is a tautology. $\text{F3}$ is a contradiction. $\text{F1} \mathrm{v} \text{F2}$ is a tautology.
GO Classes
asked
in
Mathematical Logic
Mar 26, 2023
by
GO Classes
1.5k
views
goclasses2024_wq5
goclasses
mathematical-logic
propositional-logic
multiple-selects
2-marks
49
votes
11
answers
79
GATE CSE 2009 | Question: 2
What is the chromatic number of an $n$ vertex simple connected graph which does not contain any odd length cycle? Assume $n > 2$. $2$ $3$ $n-1$ $n$
gatecse
asked
in
Graph Theory
Sep 15, 2014
by
gatecse
13.1k
views
gatecse-2009
graph-theory
graph-coloring
normal
49
votes
5
answers
80
GATE CSE 2001 | Question: 2.3
Let $f: A \rightarrow B$ a function, and let E and F be subsets of $A$. Consider the following statements about images. $S_1: f(E \cup F) = f(E) \cup f(F)$ $S_2: f(E \cap F)=f(E) \cap f(F)$ Which of the following is true about S1 and S2? Only $S_1$ is correct Only $S_2$ is correct Both $S_1$ and $S_2$ are correct None of $S_1$ and $S_2$ is correct
Kathleen
asked
in
Set Theory & Algebra
Sep 14, 2014
by
Kathleen
11.1k
views
gatecse-2001
set-theory&algebra
functions
normal
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