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Highest voted questions in Discrete Mathematics
37
votes
8
answers
161
GATE IT 2005 | Question: 31
Let $f$ be a function from a set $A$ to a set $B$, $g$ a function from $B$ to $C$, and $h$ a function from $A$ to $C$, such that $h(a) = g(f(a))$ for all $a ∈ A.$ Which of the following statements is always true for all such functions $f$ and $g$? ... is onto $h$ is onto $\implies$ $f$ is onto $h$ is onto $\implies$ $g$ is onto $h$ is onto $\implies$ $f$ and $g$ are onto
Ishrat Jahan
asked
in
Set Theory & Algebra
Nov 3, 2014
by
Ishrat Jahan
8.8k
views
gateit-2005
set-theory&algebra
functions
normal
37
votes
3
answers
162
GATE IT 2004 | Question: 4
Let $R_{1}$ be a relation from $A = \left \{ 1,3,5,7 \right \}$ to $B = \left \{ 2,4,6,8 \right \}$ and $R_{2}$ be another relation from $B$ to $C = \{1, 2, 3, 4\}$ as defined below: An element $x$ in $A$ is related to an element $y$ in $B$ (under $R_{1}$) if $x + y$ is ... $R_{1}R_{2} = \{(3, 2), (3, 4), (5, 1), (5, 3), (7, 1)\} $
Ishrat Jahan
asked
in
Set Theory & Algebra
Nov 1, 2014
by
Ishrat Jahan
10.1k
views
gateit-2004
set-theory&algebra
relations
normal
37
votes
7
answers
163
GATE IT 2006 | Question: 11
If all the edge weights of an undirected graph are positive, then any subset of edges that connects all the vertices and has minimum total weight is a Hamiltonian cycle grid hypercube tree
Ishrat Jahan
asked
in
Graph Theory
Oct 31, 2014
by
Ishrat Jahan
8.7k
views
gateit-2006
graph-theory
graph-connectivity
normal
37
votes
11
answers
164
GATE CSE 2014 Set 3 | Question: 53
The CORRECT formula for the sentence, "not all Rainy days are Cold" is $\forall d (\text{Rainy}(d) \wedge \text{~Cold}(d))$ $\forall d ( \text{~Rainy}(d) \to \text{Cold}(d))$ $\exists d(\text{~Rainy}(d) \to \text{Cold}(d))$ $\exists d(\text{Rainy}(d) \wedge \text{~Cold}(d))$
go_editor
asked
in
Mathematical Logic
Sep 28, 2014
by
go_editor
7.8k
views
gatecse-2014-set3
mathematical-logic
easy
first-order-logic
37
votes
7
answers
165
GATE CSE 2004 | Question: 77
The minimum number of colours required to colour the following graph, such that no two adjacent vertices are assigned the same color, is $2$ $3$ $4$ $5$
Kathleen
asked
in
Graph Theory
Sep 18, 2014
by
Kathleen
12.6k
views
gatecse-2004
graph-theory
graph-coloring
easy
37
votes
8
answers
166
GATE CSE 2006 | Question: 28
A logical binary relation $\odot$ ... $(\sim A\odot B)$ $\sim(A \odot \sim B)$ $\sim(\sim A\odot\sim B)$ $\sim(\sim A\odot B)$
Rucha Shelke
asked
in
Set Theory & Algebra
Sep 18, 2014
by
Rucha Shelke
5.8k
views
gatecse-2006
set-theory&algebra
binary-operation
37
votes
6
answers
167
GATE CSE 2014 Set 1 | Question: 1
Consider the statement "Not all that glitters is gold Predicate glitters$(x)$ is true if $x$ glitters and predicate gold$(x)$ is true if $x$ ... $\exists x: \text{glitters}(x)\wedge \neg \text{gold}(x)$
gatecse
asked
in
Mathematical Logic
Sep 15, 2014
by
gatecse
6.6k
views
gatecse-2014-set1
mathematical-logic
first-order-logic
37
votes
4
answers
168
GATE CSE 2000 | Question: 2.4
A polynomial $p(x)$ satisfies the following: $p(1) = p(3) = p(5) = 1$ $p(2) = p(4) = -1$ The minimum degree of such a polynomial is $1$ $2$ $3$ $4$
Kathleen
asked
in
Set Theory & Algebra
Sep 14, 2014
by
Kathleen
7.7k
views
gatecse-2000
set-theory&algebra
normal
polynomials
36
votes
6
answers
169
GATE CSE 2017 Set 2 | Question: 21
Consider the set $X=\{a, b, c, d, e\}$ under 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 ______
khushtak
asked
in
Set Theory & Algebra
Feb 14, 2017
by
khushtak
11.8k
views
gatecse-2017-set2
set-theory&algebra
lattice
numerical-answers
normal
36
votes
8
answers
170
GATE CSE 1987 | Question: 10b
What is the generating function $G(z)$ for the sequence of Fibonacci numbers?
makhdoom ghaya
asked
in
Combinatory
Nov 14, 2016
by
makhdoom ghaya
9.8k
views
gate1987
combinatory
generating-functions
descriptive
36
votes
5
answers
171
GATE CSE 2007 | Question: 85
Suppose that a robot is placed on the Cartesian plane. At each step it is allowed to move either one unit up or one unit right, i.e., if it is at $(i,j)$ then it can move to either $(i + 1, j)$ or $(i,j + 1)$. Suppose that the robot is not allowed to traverse the ... $^{20}\mathrm{C}_{10} - ^{8}\mathrm{C}_{4}\times ^{11}\mathrm{C}_{5}$
go_editor
asked
in
Combinatory
Apr 23, 2016
by
go_editor
9.4k
views
gatecse-2007
combinatory
normal
discrete-mathematics
36
votes
4
answers
172
GATE CSE 2014 Set 1 | Question: 52
An ordered $n-$tuple $(d_1, d_2,\ldots,d_n)$ with $d_1 \geq d_2 \geq \ldots \geq d_n$ is called graphic if there exists a simple undirected graph with $n$ vertices having degrees $d_1,d_2,\ldots,d_n$ respectively. Which one of the following $6$-tuples is NOT graphic? $(1,1,1,1,1,1)$ $(2,2,2,2,2,2)$ $(3,3,3,1,0,0)$ $(3,2,1,1,1,0)$
go_editor
asked
in
Graph Theory
Sep 28, 2014
by
go_editor
7.4k
views
gatecse-2014-set1
graph-theory
normal
degree-of-graph
36
votes
6
answers
173
GATE CSE 2005 | Question: 7
The time complexity of computing the transitive closure of a binary relation on a set of $n$ elements is known to be: $O(n)$ $O(n \log n)$ $O \left( n^{\frac{3}{2}} \right)$ $O\left(n^3\right)$
Kathleen
asked
in
Set Theory & Algebra
Sep 22, 2014
by
Kathleen
24.5k
views
gatecse-2005
set-theory&algebra
normal
relations
36
votes
4
answers
174
GATE CSE 2006 | Question: 2
Let $X,Y,Z$ be sets of sizes $x, y$ and $z$ respectively. Let $W = X \times Y$ and $E$ be the set of all subsets of $W$. The number of functions from $Z$ to $E$ is $z^{2^{xy}}$ $z \times 2^{xy}$ $z^{2^{x+y}}$ $2^{xyz}$
Rucha Shelke
asked
in
Set Theory & Algebra
Sep 16, 2014
by
Rucha Shelke
7.0k
views
gatecse-2006
set-theory&algebra
normal
functions
35
votes
6
answers
175
GATE CSE 2021 Set 1 | Question: 36
Let $G=(V, E)$ be an undirected unweighted connected graph. The diameter of $G$ is defined as: $\text{diam}(G)=\displaystyle \max_{u,v\in V} \{\text{the length of shortest path between $u$ and $v$}\}$ Let $M$ be the adjacency matrix of $G$. Define graph $G_2$ ... $\text{diam}(G_2) = \text{diam}(G)$ $\text{diam}(G)< \text{diam}(G_2)\leq 2\; \text{diam}(G)$
Arjun
asked
in
Graph Theory
Feb 18, 2021
by
Arjun
9.8k
views
gatecse-2021-set1
graph-theory
graph-connectivity
2-marks
34
votes
5
answers
176
TIFR CSE 2016 | Part A | Question: 15
In a tournament with $7$ teams, each team plays one match with every other team. For each match, the team earns two points if it wins, one point if it ties, and no points if it loses. At the end of all matches, the teams are ordered in the descending ... of points a team must earn in order to be guaranteed a place in the next round? $13$ $12$ $11$ $10$ $9$
go_editor
asked
in
Combinatory
Dec 28, 2016
by
go_editor
5.8k
views
tifr2016
combinatory
pigeonhole-principle
normal
34
votes
3
answers
177
GATE CSE 2015 Set 1 | Question: 14
Which one of the following is NOT equivalent to $p ↔ q$? $(\neg p ∨ q) ∧ (p ∨ \neg q)$ $(\neg p ∨ q) ∧ (q → p)$ $(\neg p ∧ q) ∨ ( p ∧ \neg q)$ $(\neg p ∧ \neg q) ∨ (p ∧ q)$
makhdoom ghaya
asked
in
Mathematical Logic
Feb 12, 2015
by
makhdoom ghaya
7.5k
views
gatecse-2015-set1
mathematical-logic
easy
propositional-logic
34
votes
2
answers
178
GATE IT 2004 | Question: 37
What is the number of vertices in an undirected connected graph with $27$ edges, $6$ vertices of degree $2, 3$ vertices of degree $4$ and remaining of degree $3$? $10$ $11$ $18$ $19$
Ishrat Jahan
asked
in
Graph Theory
Nov 2, 2014
by
Ishrat Jahan
12.9k
views
gateit-2004
graph-theory
graph-connectivity
normal
34
votes
5
answers
179
GATE IT 2006 | Question: 6
Given a boolean function $f (x_1, x_2, \ldots, x_n),$ which of the following equations is NOT true? $f (x_1, x_2, \ldots, x_n) = x_1'f(x_1, x_2, \ldots, x_n) + x_1f(x_1, x_2, \ldots, x_n)$ ... $f (x_1, x_2, \ldots , x_n) = f(0, x_2, , x_n) + f(1, x_2, \ldots, x_n)$
Ishrat Jahan
asked
in
Set Theory & Algebra
Oct 31, 2014
by
Ishrat Jahan
6.2k
views
gateit-2006
set-theory&algebra
functions
normal
34
votes
4
answers
180
GATE IT 2008 | Question: 3
What is the chromatic number of the following graph? $2$ $3$ $4$ $5$
Ishrat Jahan
asked
in
Graph Theory
Oct 27, 2014
by
Ishrat Jahan
8.2k
views
gateit-2008
graph-theory
graph-coloring
normal
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