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Hot questions in Discrete Mathematics
44
votes
10
answers
31
GATE CSE 2016 Set 2 | Question: 29
The value of the expression $13^{99}\pmod{17}$ in the range $0$ to $16$, is ________.
The value of the expression $13^{99}\pmod{17}$ in the range $0$ to $16$, is ________.
Akash Kanase
17.9k
views
Akash Kanase
asked
Feb 12, 2016
Combinatory
gatecse-2016-set2
modular-arithmetic
normal
numerical-answers
+
–
85
votes
8
answers
32
GATE CSE 2016 Set 2 | Question: 28
Consider a set $U$ of $23$ different compounds in a chemistry lab. There is a subset $S$ of $U$ of $9$ compounds, each of which reacts with exactly $3$ compounds of $U$. Consider the following statements: Each compound in U \ S reacts ... \ S reacts with an even number of compounds. Which one of the above statements is ALWAYS TRUE? Only I Only II Only III None.
Consider a set $U$ of $23$ different compounds in a chemistry lab. There is a subset $S$ of $U$ of $9$ compounds, each of which reacts with exactly $3$ compounds of $U$. ...
Akash Kanase
16.7k
views
Akash Kanase
asked
Feb 12, 2016
Set Theory & Algebra
gatecse-2016-set2
set-theory&algebra
difficult
set-theory
+
–
78
votes
6
answers
33
GATE CSE 1992 | Question: 92,xv
Which of the following predicate calculus statements is/are valid? $(\forall (x)) P(x) \vee (\forall(x))Q(x) \implies (\forall (x)) (P(x) \vee Q(x))$ $(\exists (x)) P(x) \wedge (\exists (x))Q(x) \implies (\exists (x)) (P(x) \wedge Q(x))$ ... $(\exists (x)) (P(x) \vee Q(x)) \implies \sim (\forall (x)) P(x) \vee (\exists (x)) Q(x)$
Which of the following predicate calculus statements is/are valid?$(\forall (x)) P(x) \vee (\forall(x))Q(x) \implies (\forall (x)) (P(x) \vee Q(x))$$(\exists (x)) P(x) \w...
Arjun
16.6k
views
Arjun
asked
Sep 2, 2014
Mathematical Logic
gate1992
mathematical-logic
normal
first-order-logic
+
–
74
votes
8
answers
34
GATE CSE 2016 Set 1 | Question: 1
Let $p, q, r, s$ represents the following propositions. $p:x\in\left\{8, 9, 10, 11, 12\right\}$ $q:$ $x$ is a composite number. $r:$ $x$ is a perfect square. $s:$ $x$ is a prime number. The integer $x\geq2$ which satisfies $\neg\left(\left(p\Rightarrow q\right) \wedge \left(\neg r \vee \neg s\right)\right)$ is ____________.
Let $p, q, r, s$ represents the following propositions.$p:x\in\left\{8, 9, 10, 11, 12\right\}$$q:$ $x$ is a composite number.$r:$ $x$ is a perfect square.$s:$ $x$ is a pr...
Sandeep Singh
13.1k
views
Sandeep Singh
asked
Feb 12, 2016
Mathematical Logic
gatecse-2016-set1
mathematical-logic
normal
numerical-answers
propositional-logic
+
–
26
votes
6
answers
35
GATE CSE 2021 Set 2 | Question: 50
Let $S$ be a set of 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 ___________
Let $S$ be a set of 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 ___________
Arjun
12.0k
views
Arjun
asked
Feb 18, 2021
Combinatory
gatecse-2021-set2
combinatory
counting
numerical-answers
2-marks
+
–
59
votes
7
answers
36
GATE CSE 2003 | Question: 32
Which of the following is a valid first order formula? (Here \(\alpha\) and \(\beta\) are first order formulae with $x$ as their only free variable) $((∀x)[α] ⇒ (∀x)[β]) ⇒ (∀x)[α ⇒ β]$ $(∀x)[α] ⇒ (∃x)[α ∧ β]$ $((∀x)[α ∨ β] ⇒ (∃x)[α]) ⇒ (∀x)[α]$ $(∀x)[α ⇒ β] ⇒ (((∀x)[α]) ⇒ (∀x)[β])$
Which of the following is a valid first order formula? (Here \(\alpha\) and \(\beta\) are first order formulae with $x$ as their only free variable)$((∀x)[α] ⇒ (∀x...
Kathleen
16.9k
views
Kathleen
asked
Sep 16, 2014
Mathematical Logic
gatecse-2003
mathematical-logic
first-order-logic
normal
+
–
40
votes
6
answers
37
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
20.5k
views
Arjun
asked
Feb 7, 2019
Graph Theory
gatecse-2019
engineering-mathematics
discrete-mathematics
graph-theory
graph-connectivity
2-marks
+
–
78
votes
6
answers
38
GATE CSE 2014 Set 3 | Question: 49
Consider the set of all functions $f:\{0,1, \dots,2014\} \to \{0,1,\dots, 2014\}$ such that $ f\left(f\left(i\right)\right)=i$, for all $0 \leq i \leq 2014$. Consider the following statements: $P$. For each such function it must be the case that for every ... is CORRECT? $P, Q$ and $R$ are true Only $Q$ and $R$ are true Only $P$ and $Q$ are true Only $R$ is true
Consider the set of all functions $f:\{0,1, \dots,2014\} \to \{0,1,\dots, 2014\}$ such that $ f\left(f\left(i\right)\right)=i$, for all $0 \leq i \leq 2014$. Consider th...
go_editor
15.7k
views
go_editor
asked
Sep 28, 2014
Set Theory & Algebra
gatecse-2014-set3
set-theory&algebra
functions
normal
+
–
28
votes
6
answers
39
GATE CSE 2020 | Question: 52
Graph $G$ is obtained by adding vertex $s$ to $K_{3,4}$ and making $s$ adjacent to every vertex of $K_{3,4}$. The minimum number of colours required to edge-colour $G$ is _______
Graph $G$ is obtained by adding vertex $s$ to $K_{3,4}$ and making $s$ adjacent to every vertex of $K_{3,4}$. The minimum number of colours required to edge-colour $G$ is...
Arjun
13.7k
views
Arjun
asked
Feb 12, 2020
Graph Theory
gatecse-2020
numerical-answers
graph-theory
graph-coloring
2-marks
+
–
28
votes
8
answers
40
GATE CSE 2020 | Question: 42
The number of permutations of the characters in LILAC so that no character appears in its original position, if the two L’s are indistinguishable, is ______.
The number of permutations of the characters in LILAC so that no character appears in its original position, if the two L’s are indistinguishable, is ______.
Arjun
16.6k
views
Arjun
asked
Feb 12, 2020
Combinatory
gatecse-2020
numerical-answers
combinatory
2-marks
+
–
66
votes
6
answers
41
GATE CSE 2015 Set 1 | Question: 16
For a set $A$, the power set of $A$ is denoted by $2^{A}$. If $A = \left\{5,\left\{6\right\}, \left\{7\right\}\right\}$, which of the following options are TRUE? $\varnothing \in 2^{A}$ $\varnothing \subseteq 2^{A}$ ... I and III only II and III only I, II and III only I, II and IV only
For a set $A$, the power set of $A$ is denoted by $2^{A}$. If $A = \left\{5,\left\{6\right\}, \left\{7\right\}\right\}$, which of the following options are TRUE?$\varnoth...
makhdoom ghaya
15.6k
views
makhdoom ghaya
asked
Feb 13, 2015
Set Theory & Algebra
gatecse-2015-set1
set-theory&algebra
set-theory
normal
+
–
42
votes
11
answers
42
GATE CSE 2018 | Question: 1
Which one of the following is a closed form expression for the generating function of the sequence $\{a_n\}$, where $a_n = 2n +3 \text{ for all } n=0, 1, 2, \dots$? $\frac{3}{(1-x)^2}$ $\frac{3x}{(1-x)^2}$ $\frac{2-x}{(1-x)^2}$ $\frac{3-x}{(1-x)^2}$
Which one of the following is a closed form expression for the generating function of the sequence $\{a_n\}$, where $a_n = 2n +3 \text{ for all } n=0, 1, 2, \dots$?$\frac...
gatecse
22.8k
views
gatecse
asked
Feb 14, 2018
Combinatory
gatecse-2018
generating-functions
normal
combinatory
1-mark
+
–
68
votes
10
answers
43
GATE CSE 2019 | Question: 35
Consider the first order predicate formula $\varphi$: $\forall x [ ( \forall z \: z | x \Rightarrow (( z=x) \vee (z=1))) \rightarrow \exists w ( w > x) \wedge (\forall z \: z | w \Rightarrow ((w=z) \vee (z=1)))]$ Here $a \mid b$ denotes ... of all integers Which of the above sets satisfy $\varphi$? $S_1$ and $S_2$ $S_1$ and $S_3$ $S_2$ and $S_3$ $S_1, S_2$ and $S_3$
Consider the first order predicate formula $\varphi$:$\forall x [ ( \forall z \: z | x \Rightarrow (( z=x) \vee (z=1))) \rightarrow \exists w ( w x) \wedge (\forall z \:...
Arjun
20.2k
views
Arjun
asked
Feb 7, 2019
Mathematical Logic
gatecse-2019
engineering-mathematics
discrete-mathematics
mathematical-logic
first-order-logic
2-marks
+
–
77
votes
8
answers
44
GATE CSE 2014 Set 2 | Question: 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 the symmetric difference of the two sets is in $U$. Consider the ... $S1$ is true and $S2$ is false $S2$ is true and $S1$ is false Neither $S1$ nor $S2$ is true
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 ...
go_editor
15.9k
views
go_editor
asked
Sep 28, 2014
Set Theory & Algebra
gatecse-2014-set2
set-theory&algebra
normal
set-theory
+
–
86
votes
8
answers
45
GATE CSE 2004 | Question: 79
How many graphs on $n$ labeled vertices exist which have at least $\frac{(n^2 - 3n)}{ 2}$ edges ? $^{\left(\frac{n^2-n}{2}\right)}C_{\left(\frac{n^2-3n} {2}\right)}$ $^{{\large\sum\limits_{k=0}^{\left (\frac{n^2-3n}{2} \right )}}.\left(n^2-n\right)}C_k$ $^{\left(\frac{n^2-n}{2}\right)}C_n$ $^{{\large\sum\limits_{k=0}^n}.\left(\frac{n^2-n}{2}\right)}C_k$
How many graphs on $n$ labeled vertices exist which have at least $\frac{(n^2 - 3n)}{ 2}$ edges ?$^{\left(\frac{n^2-n}{2}\right)}C_{\left(\frac{n^2-3n} {2}\right)}$$^{{\l...
Kathleen
14.5k
views
Kathleen
asked
Sep 18, 2014
Graph Theory
gatecse-2004
graph-theory
combinatory
normal
counting
+
–
58
votes
7
answers
46
GATE IT 2008 | Question: 4
What is the size of the smallest $\textsf{MIS}$ (Maximal Independent Set) of a chain of nine nodes? $5$ $4$ $3$ $2$
What is the size of the smallest $\textsf{MIS}$ (Maximal Independent Set) of a chain of nine nodes?$5$$4$$3$$2$
Ishrat Jahan
59.0k
views
Ishrat Jahan
asked
Oct 27, 2014
Graph Theory
gateit-2008
normal
graph-connectivity
+
–
24
votes
6
answers
47
GATE CSE 1995 | Question: 1.20
The number of elements in the power set $P(S)$ of the set $S=\{\{\emptyset\}, 1, \{2, 3\}\}$ is: $2$ $4$ $8$ None of the above
The number of elements in the power set $P(S)$ of the set $S=\{\{\emptyset\}, 1, \{2, 3\}\}$ is:$2$$4$$8$None of the above
Kathleen
16.3k
views
Kathleen
asked
Oct 8, 2014
Set Theory & Algebra
gate1995
set-theory&algebra
normal
set-theory
+
–
77
votes
6
answers
48
GATE CSE 2014 Set 3 | Question: 50
There are two elements $x,\:y$ in a group $(G,*)$ such that every element in the group can be written as a product of some number of $x$'s and $y$'s in some order. It is known that $x*x=y*y=x*y*x*y=y*x*y*x=e$ where $e$ is the identity element. The maximum number of elements in such a group is ____.
There are two elements $x,\:y$ in a group $(G,*)$ such that every element in the group can be written as a product of some number of $x$'s and $y$'s in some order. It is ...
go_editor
15.7k
views
go_editor
asked
Sep 28, 2014
Set Theory & Algebra
gatecse-2014-set3
set-theory&algebra
group-theory
numerical-answers
normal
+
–
63
votes
7
answers
49
GATE IT 2006 | Question: 21
Consider the following first order logic formula in which $R$ is a binary relation symbol. $∀x∀y (R(x, y) \implies R(y, x))$ The formula is satisfiable and valid satisfiable and so is its negation unsatisfiable but its negation is valid satisfiable but its negation is unsatisfiable
Consider the following first order logic formula in which $R$ is a binary relation symbol.$∀x∀y (R(x, y) \implies R(y, x))$The formula issatisfiable and validsatisfia...
Ishrat Jahan
13.4k
views
Ishrat Jahan
asked
Oct 31, 2014
Mathematical Logic
gateit-2006
mathematical-logic
normal
first-order-logic
+
–
50
votes
9
answers
50
GATE IT 2005 | Question: 36
Let $P(x)$ and $Q(x)$ ...
Let $P(x)$ and $Q(x)$ be arbitrary predicates. Which of the following statements is always TRUE?$\left(\left(\forall x \left(P\left(x\right) \vee Q\left(x\right)\right)\r...
Ishrat Jahan
14.9k
views
Ishrat Jahan
asked
Nov 3, 2014
Mathematical Logic
gateit-2005
mathematical-logic
first-order-logic
normal
+
–
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