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Featured
Highest voted questions in Discrete Mathematics
42
votes
2
answers
121
GATE CSE 1997 | Question: 6.1
A partial order $≤$ is defined on the set $S=\left \{ x, a_1, a_2, \ldots, a_n, y \right \}$ as $x$ $\leq _{i}$ $a_{i}$ for all $i$ and $a_{i}\leq y$ for all $i$, where $n ≥ 1$. The number of total orders on the set S which contain the partial order $≤$ is $n!$ $n+2$ $n$ $1$
A partial order $≤$ is defined on the set $S=\left \{ x, a_1, a_2, \ldots, a_n, y \right \}$ as $x$ $\leq _{i}$ $a_{i}$ for all $i$ and $a_{i}\leq y$ for all $i$, where...
Kathleen
8.9k
views
Kathleen
asked
Sep 29, 2014
Set Theory & Algebra
gate1997
set-theory&algebra
partial-order
normal
+
–
42
votes
6
answers
122
GATE CSE 2014 Set 2 | Question: 51
A cycle on $n$ vertices is isomorphic to its complement. The value of $n$ is _____.
A cycle on $n$ vertices is isomorphic to its complement. The value of $n$ is _____.
go_editor
17.6k
views
go_editor
asked
Sep 28, 2014
Graph Theory
gatecse-2014-set2
graph-theory
numerical-answers
normal
graph-isomorphism
non-gate
+
–
42
votes
8
answers
123
GATE CSE 2004 | Question: 73
The inclusion of which of the following sets into $S = \left\{ \left\{1, 2\right\}, \left\{1, 2, 3\right\}, \left\{1, 3, 5\right\}, \left\{1, 2, 4\right\}, \left\{1, 2, 3, 4, 5\right\} \right\} $ is necessary and sufficient to make $S$ a complete lattice under the partial order defined by ... $\{1\}, \{1, 3\}$ $\{1\}, \{1, 3\}, \{1, 2, 3, 4\}, \{1, 2, 3, 5\}$
The inclusion of which of the following sets into$S = \left\{ \left\{1, 2\right\}, \left\{1, 2, 3\right\}, \left\{1, 3, 5\right\}, \left\{1, 2, 4\right\}, \left\{1, 2, 3,...
Kathleen
13.0k
views
Kathleen
asked
Sep 18, 2014
Set Theory & Algebra
gatecse-2004
set-theory&algebra
partial-order
normal
+
–
41
votes
4
answers
124
GATE CSE 1991 | Question: 15,b
Consider the following first order formula: ... Does it have finite models? Is it satisfiable? If so, give a countable model for it.
Consider the following first order formula:$\left ( \matrix{ \forall x \exists y : R(x,y) \\[1em] \Large \land \\[1em] \forall x \forall y : \left ( R(x,y) \impl...
ibia
6.4k
views
ibia
asked
Nov 16, 2015
Mathematical Logic
gate1991
mathematical-logic
first-order-logic
descriptive
+
–
41
votes
1
answer
125
GATE IT 2004 | Question: 34
Let $H_1, H_2, H_3,$ ... be harmonic numbers. Then, for $n \in Z^+$, $\sum_{j=1}^{n} H_j$ can be expressed as $nH_{n+1} - (n + 1)$ $(n + 1)H_n - n$ $nH_n - n$ $(n + 1) H_{n+1} - (n + 1)$
Let $H_1, H_2, H_3,$ ... be harmonic numbers. Then, for $n \in Z^+$, $\sum_{j=1}^{n} H_j$ can be expressed as$nH_{n+1} - (n + 1)$$(n + 1)H_n - n$$nH_n - n$$(n + 1) H_{n+...
Ishrat Jahan
5.6k
views
Ishrat Jahan
asked
Nov 2, 2014
Combinatory
gateit-2004
recurrence-relation
combinatory
normal
+
–
41
votes
9
answers
126
GATE IT 2004 | Question: 31
Let $p, q, r$ and $s$ be four primitive statements. Consider the following arguments: $P: [(¬p\vee q) ∧ (r → s) ∧ (p \vee r)] → (¬s → q)$ $Q: [(¬p ∧q) ∧ [q → (p → r)]] → ¬r$ $R: [[(q ∧ r) → p] ∧ (¬q \vee p)] → r$ $S: [p ∧ (p → r) ∧ (q \vee ¬ r)] → q$ Which of the above arguments are valid? $P$ and $Q$ only $P$ and $R$ only $P$ and $S$ only $P, Q, R$ and $S$
Let $p, q, r$ and $s$ be four primitive statements. Consider the following arguments:$P: [(¬p\vee q) ∧ (r → s) ∧ (p \vee r)] → (¬s → q)$$Q: [(¬p ∧q) �...
Ishrat Jahan
11.9k
views
Ishrat Jahan
asked
Nov 2, 2014
Mathematical Logic
gateit-2004
mathematical-logic
normal
propositional-logic
+
–
41
votes
2
answers
127
GATE CSE 2014 Set 3 | Question: 3
Let $G$ be a group with $15$ elements. Let $L$ be a subgroup of $G$. It is known that $L \neq\ G$ and that the size of $L$ is at least $4$. The size of $L$ is __________.
Let $G$ be a group with $15$ elements. Let $L$ be a subgroup of $G$. It is known that $L \neq\ G$ and that the size of $L$ is at least $4$. The size of $L$ is __________....
go_editor
8.5k
views
go_editor
asked
Sep 28, 2014
Set Theory & Algebra
gatecse-2014-set3
set-theory&algebra
group-theory
numerical-answers
normal
+
–
41
votes
5
answers
128
GATE CSE 2012 | Question: 37
How many onto (or surjective) functions are there from an $n$-element $(n ≥ 2)$ set to a $2$-element set? $ 2^{n}$ $2^{n} – 1$ $2^{n} – 2$ $2(2^{n} – 2)$
How many onto (or surjective) functions are there from an $n$-element $(n ≥ 2)$ set to a $2$-element set?$ 2^{n}$$2^{n} – 1$$2^{n} – 2$$2(2^{n} – 2)$
gatecse
9.4k
views
gatecse
asked
Sep 26, 2014
Set Theory & Algebra
gatecse-2012
set-theory&algebra
functions
normal
+
–
41
votes
3
answers
129
GATE CSE 2007 | Question: 26
Consider the set $S =\{ a , b , c , d\}.$ Consider the following $4$ partitions $π_1,π_2,π_3,π_4$ on $S : π_1 =\{\overline{abcd}\},\quad π_2 =\{\overline{ab}, \overline{cd}\},$ ... $π_i \prec π_j$ if and only if $π_i$ refines $π_j$. The poset diagram for $(S',\prec)$ is:
Consider the set $S =\{ a , b , c , d\}.$ Consider the following $4$ partitions $π_1,π_2,π_3,π_4$ on$S : π_1 =\{\overline{abcd}\},\quad π_2 =\{\overline{ab}, \overl...
Kathleen
13.5k
views
Kathleen
asked
Sep 21, 2014
Set Theory & Algebra
gatecse-2007
set-theory&algebra
normal
partial-order
descriptive
+
–
41
votes
10
answers
130
GATE CSE 2003 | Question: 38
Consider the set \(\{a, b, c\}\) with binary operators \(+\) and \(*\) defined as follows: ... $(x, y)$ that satisfy the equations) is $0$ $1$ $2$ $3$
Consider the set \(\{a, b, c\}\) with binary operators \(+\) and \(*\) defined as follows:$$\begin{array}{|c|c|c|c|} \hline \textbf{+} & \textbf{a}& \textbf{b} &\textbf{c...
Kathleen
7.1k
views
Kathleen
asked
Sep 17, 2014
Set Theory & Algebra
gatecse-2003
set-theory&algebra
normal
binary-operation
+
–
40
votes
6
answers
131
GATE CSE 2019 | Question: 38
Let $G$ be any connected, weighted, undirected graph. $G$ has a unique minimum spanning tree, if no two edges of $G$ have the same weight. $G$ has a unique minimum spanning tree, if, for every cut of $G$, there is a unique minimum-weight edge crossing the cut. Which of the following statements is/are TRUE? I only II only Both I and II Neither I nor II
Let $G$ be any connected, weighted, undirected graph.$G$ has a unique minimum spanning tree, if no two edges of $G$ have the same weight.$G$ has a unique minimum spanning...
Arjun
20.6k
views
Arjun
asked
Feb 7, 2019
Graph Theory
gatecse-2019
engineering-mathematics
discrete-mathematics
graph-theory
graph-connectivity
2-marks
+
–
40
votes
5
answers
132
GATE CSE 2017 Set 2 | Question: 24
Consider the quadratic equation $x^2-13x+36=0$ with coefficients in a base $b$. The solutions of this equation in the same base $b$ are $x=5$ and $x=6$. Then $b=$ _____
Consider the quadratic equation $x^2-13x+36=0$ with coefficients in a base $b$. The solutions of this equation in the same base $b$ are $x=5$ and $x=6$. Then $b=$ _____
khushtak
14.5k
views
khushtak
asked
Feb 14, 2017
Set Theory & Algebra
gatecse-2017-set2
polynomials
numerical-answers
set-theory&algebra
+
–
40
votes
2
answers
133
TIFR CSE 2012 | Part A | Question: 8
How many pairs of sets $(A, B)$ are there that satisfy the condition $A, B \subseteq \left\{1, 2,...,5\right\}, A \cap B = \{\}?$ $125$ $127$ $130$ $243$ $257$
How many pairs of sets $(A, B)$ are there that satisfy the condition $A, B \subseteq \left\{1, 2,...,5\right\}, A \cap B = \{\}?$$125$$127$$130$$243$$257$
makhdoom ghaya
3.2k
views
makhdoom ghaya
asked
Oct 26, 2015
Set Theory & Algebra
tifr2012
set-theory&algebra
set-theory
+
–
40
votes
5
answers
134
TIFR CSE 2010 | Part A | Question: 18
Let $X$ be a set of size $n$. How many pairs of sets (A, B) are there that satisfy the condition $A\subseteq B \subseteq X$ ? $2^{n+1}$ $2^{2n}$ $3^{n}$ $2^{n} + 1$ $3^{n + 1}$
Let $X$ be a set of size $n$. How many pairs of sets (A, B) are there that satisfy the condition $A\subseteq B \subseteq X$ ?$2^{n+1}$$2^{2n}$$3^{n}$$2^{n} + 1$$3^{n + 1}...
makhdoom ghaya
4.7k
views
makhdoom ghaya
asked
Oct 4, 2015
Set Theory & Algebra
tifr2010
set-theory
+
–
40
votes
5
answers
135
GATE CSE 1996 | Question: 2.2
Let $R$ be a non-empty relation on a collection of sets defined by $_{A}R_ B$ if and only if $A \cap B = \phi$. Then, (pick the true statement) $A$ is reflexive and transitive $R$ is symmetric and not transitive $R$ is an equivalence relation $R$ is not reflexive and not symmetric
Let $R$ be a non-empty relation on a collection of sets defined by $_{A}R_ B$ if and only if $A \cap B = \phi$. Then, (pick the true statement)$A$ is reflexive and transi...
Kathleen
14.0k
views
Kathleen
asked
Oct 9, 2014
Set Theory & Algebra
gate1996
set-theory&algebra
relations
normal
+
–
40
votes
5
answers
136
GATE CSE 1998 | Question: 1.5
What is the converse of the following assertion? I stay only if you go I stay if you go If I stay then you go If you do not go then I do not stay If I do not stay then you go
What is the converse of the following assertion?I stay only if you goI stay if you goIf I stay then you goIf you do not go then I do not stayIf I do not stay then you go
Kathleen
14.0k
views
Kathleen
asked
Sep 25, 2014
Mathematical Logic
gate1998
mathematical-logic
easy
propositional-logic
+
–
40
votes
7
answers
137
GATE CSE 2005 | Question: 43
Let $f: B \to C$ and $g: A \to B$ be two functions and let $h = f o g$. Given that $h$ is an onto function which one of the following is TRUE? $f$ and $g$ should both be onto functions $f$ should be onto but $g$ need not to be onto $g$ should be onto but $f$ need not be onto both $f$ and $g$ need not be onto
Let $f: B \to C$ and $g: A \to B$ be two functions and let $h = f o g$. Given that $h$ is an onto function which one of the following is TRUE?$f$ and $g$ should both be o...
gatecse
10.0k
views
gatecse
asked
Sep 21, 2014
Set Theory & Algebra
gatecse-2005
set-theory&algebra
functions
normal
+
–
40
votes
7
answers
138
GATE CSE 2010 | Question: 28
The degree sequence of a simple graph is the sequence of the degrees of the nodes in the graph in decreasing order. Which of the following sequences can not be the degree sequence of any graph? $7, 6, 5, 4, 4, 3, 2, 1$ $6, 6, 6, 6, 3, 3, 2, 2$ $7, 6, 6, 4, 4, 3, 2, 2$ $8, 7, 7, 6, 4, 2, 1, 1$ I and II III and IV IV only II and IV
The degree sequence of a simple graph is the sequence of the degrees of the nodes in the graph in decreasing order. Which of the following sequences can not be the degree...
gatecse
18.6k
views
gatecse
asked
Sep 21, 2014
Graph Theory
gatecse-2010
graph-theory
degree-of-graph
+
–
40
votes
4
answers
139
GATE CSE 2004 | Question: 72
The following is the incomplete operation table of a $4-$ ... last row of the table is $c\;a\;e\; b$ $c\; b\; a\; e$ $c\; b\; e\; a$ $c\; e\; a\; b$
The following is the incomplete operation table of a $4-$element group.$$\begin{array}{|l|l|l|l|l|} \hline \textbf{*} & \textbf{e}& \textbf{a} &\textbf{b} & \textbf{c}\\\...
Kathleen
6.8k
views
Kathleen
asked
Sep 18, 2014
Set Theory & Algebra
gatecse-2004
set-theory&algebra
group-theory
normal
+
–
40
votes
8
answers
140
GATE CSE 2009 | Question: 23
Which one of the following is the most appropriate logical formula to represent the statement? "Gold and silver ornaments are precious". The following notations are used: $G(x): x$ is a gold ornament $S(x): x$ is a silver ornament $P(x): x$ ... $\forall x((G(x) \vee S(x)) \implies P(x))$
Which one of the following is the most appropriate logical formula to represent the statement?"Gold and silver ornaments are precious".The following notations are used: ...
gatecse
8.6k
views
gatecse
asked
Sep 15, 2014
Mathematical Logic
gatecse-2009
mathematical-logic
easy
first-order-logic
+
–
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