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Hot questions in Discrete Mathematics
33
votes
8
answers
61
GATE IT 2008 | Question: 28
Consider the following Hasse diagrams. Which all of the above represent a lattice? (i) and (iv) only (ii) and (iii) only (iii) only (i), (ii) and (iv) only
Ishrat Jahan
asked
in
Set Theory & Algebra
Oct 28, 2014
by
Ishrat Jahan
15.0k
views
gateit-2008
set-theory&algebra
lattice
normal
52
votes
8
answers
62
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
63
votes
5
answers
63
GATE CSE 2014 Set 3 | Question: 2
Let $X$ and $Y$ be finite sets and $f:X \to Y$ be a function. Which one of the following statements is TRUE? For any subsets $A$ and $B$ of $X, |f(A \cup B)| = |f(A)| + |f(B)|$ For any subsets $A$ and $B$ of $X, f(A \cap B) = f(A) \cap f(B)$ For any subsets $A$ ... $S$ and $T$ of $Y, f^{-1}(S \cap T) = f^{-1}(S) \cap f^{-1}(T)$
go_editor
asked
in
Set Theory & Algebra
Sep 28, 2014
by
go_editor
14.0k
views
gatecse-2014-set3
set-theory&algebra
functions
normal
14
votes
8
answers
64
GATE CSE 2021 Set 1 | Question: 7
Let $p$ and $q$ be two propositions. Consider the following two formulae in propositional logic. $S_1: (\neg p\wedge(p\vee q))\rightarrow q$ $S_2: q\rightarrow(\neg p\wedge(p\vee q))$ Which one of the following choices is correct? Both $S_1$ and ... but $S_2$ is not a tautology $S_1$ is not a tautology but $S_2$ is a tautology Neither $S_1$ nor $S_2$ is a tautology
Arjun
asked
in
Mathematical Logic
Feb 18, 2021
by
Arjun
8.1k
views
gatecse-2021-set1
mathematical-logic
propositional-logic
1-mark
60
votes
6
answers
65
GATE CSE 2000 | Question: 2.6
Let $P(S)$ denotes the power set of set $S.$ Which of the following is always true? $P(P(S)) = P(S)$ $P(S) ∩ P(P(S)) = \{ Ø \}$ $P(S) ∩ S = P(S)$ $S ∉ P(S)$
Kathleen
asked
in
Set Theory & Algebra
Sep 14, 2014
by
Kathleen
13.4k
views
gatecse-2000
set-theory&algebra
easy
set-theory
62
votes
6
answers
66
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
Ishrat Jahan
asked
in
Mathematical Logic
Oct 31, 2014
by
Ishrat Jahan
13.3k
views
gateit-2006
mathematical-logic
normal
first-order-logic
27
votes
9
answers
67
GATE CSE 2021 Set 2 | Question: 15
Choose the correct choice(s) regarding the following proportional logic assertion $S$: $S: (( P \wedge Q) \rightarrow R) \rightarrow (( P \wedge Q) \rightarrow (Q \rightarrow R))$ $S$ is neither a tautology nor a contradiction $S$ is a tautology $S$ is a contradiction The antecedent of $S$ is logically equivalent to the consequent of $S$
Arjun
asked
in
Mathematical Logic
Feb 18, 2021
by
Arjun
8.7k
views
gatecse-2021-set2
multiple-selects
mathematical-logic
propositional-logic
1-mark
26
votes
6
answers
68
GATE CSE 2022 | Question: 26
Which one of the following is the closed form for the generating function of the sequence $\{ a_{n} \}_{n \geq 0}$ defined below? $ a_{n} = \left\{\begin{matrix} n + 1, & \text{n is odd} & \\ 1, & \text{otherwise} & \end{matrix}\right.$ ... $\frac{2x}{(1-x^{2})^{2}} + \frac{1}{1-x}$ $\frac{x}{(1-x^{2})^{2}} + \frac{1}{1-x}$
Arjun
asked
in
Combinatory
Feb 15, 2022
by
Arjun
9.3k
views
gatecse-2022
combinatory
generating-functions
2-marks
57
votes
10
answers
69
GATE CSE 2017 Set 2 | Question: 11
Let $p, q, r$ ... $(\neg p \wedge r) \vee (r \rightarrow (p \wedge q))$
khushtak
asked
in
Mathematical Logic
Feb 14, 2017
by
khushtak
12.1k
views
gatecse-2017-set2
mathematical-logic
propositional-logic
25
votes
9
answers
70
GATE CSE 2017 Set 1 | Question: 47
The number of integers between $1$ and $500$ (both inclusive) that are divisible by $3$ or $5$ or $7$ is ____________ .
Arjun
asked
in
Set Theory & Algebra
Feb 14, 2017
by
Arjun
11.6k
views
gatecse-2017-set1
set-theory&algebra
normal
numerical-answers
set-theory
51
votes
12
answers
71
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
60
votes
9
answers
72
GATE CSE 2005 | Question: 44
What is the minimum number of ordered pairs of non-negative numbers that should be chosen to ensure that there are two pairs $(a,b)$ and $(c,d)$ in the chosen set such that, $a \equiv c\mod 3$ and $b \equiv d \mod 5$ $4$ $6$ $16$ $24$
gatecse
asked
in
Combinatory
Sep 21, 2014
by
gatecse
13.3k
views
gatecse-2005
set-theory&algebra
normal
pigeonhole-principle
39
votes
5
answers
73
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
Kathleen
asked
in
Mathematical Logic
Sep 25, 2014
by
Kathleen
13.8k
views
gate1998
mathematical-logic
easy
propositional-logic
39
votes
5
answers
74
GATE CSE 2000 | Question: 2.5
A relation $R$ is defined on the set of integers as $xRy$ iff $(x + y)$ is even. Which of the following statements is true? $R$ is not an equivalence relation $R$ is an equivalence relation having $1$ equivalence class $R$ is an equivalence relation having $2$ equivalence classes $R$ is an equivalence relation having $3$ equivalence classes
Kathleen
asked
in
Set Theory & Algebra
Sep 14, 2014
by
Kathleen
14.0k
views
gatecse-2000
set-theory&algebra
relations
normal
14
votes
3
answers
75
GATE CSE 2022 | Question: 27
Consider a simple undirected unweighted graph with at least three vertices. If $\textit{A}$ is the adjacency matrix of the graph, then the number of $3–$cycles in the graph is given by the trace of $\textit{A}^{3}$ $\textit{A}^{3}$ divided by $2$ $\textit{A}^{3}$ divided by $3$ $\textit{A}^{3}$ divided by $6$
Arjun
asked
in
Graph Theory
Feb 15, 2022
by
Arjun
7.4k
views
gatecse-2022
graph-theory
graph-connectivity
2-marks
64
votes
9
answers
76
GATE IT 2006 | Question: 25
Consider the undirected graph $G$ defined as follows. The vertices of $G$ are bit strings of length $n$. We have an edge between vertex $u$ and vertex $v$ if and only if $u$ and $v$ differ in exactly one bit position (in other words, $v$ can be obtained from $u$ by ... $\left(\frac{1}{n}\right)$ $\left(\frac{2}{n}\right)$ $\left(\frac{3}{n}\right)$
Ishrat Jahan
asked
in
Graph Theory
Oct 31, 2014
by
Ishrat Jahan
13.1k
views
gateit-2006
graph-theory
graph-coloring
normal
40
votes
5
answers
77
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
Kathleen
asked
in
Set Theory & Algebra
Oct 9, 2014
by
Kathleen
13.9k
views
gate1996
set-theory&algebra
relations
normal
1
vote
2
answers
78
UGC NET CSE | December 2006 | Part 2 | Question: 3
The number of edges in a complete graph with $N$ vertices is equal to : $N (N−1)$ $2N−1$ $N−1$ $N(N−1)/2$
go_editor
asked
in
Graph Theory
Mar 27, 2020
by
go_editor
12.0k
views
ugcnetcse-dec2006-paper2
76
votes
6
answers
79
GATE CSE 2008 | Question: 42
$G$ is a graph on $n$ vertices and $2n-2$ edges. The edges of $G$ can be partitioned into two edge-disjoint spanning trees. Which of the following is NOT true for $G$? For every subset of $k$ vertices, the induced subgraph has at ... least $2$ edge-disjoint paths between every pair of vertices. There are at least $2$ vertex-disjoint paths between every pair of vertices.
Akshay Jindal
asked
in
Graph Theory
Sep 27, 2014
by
Akshay Jindal
23.4k
views
gatecse-2008
graph-connectivity
normal
28
votes
6
answers
80
GATE CSE 1995 | Question: 1.19
Let $R$ be a symmetric and transitive relation on a set $A$. Then $R$ is reflexive and hence an equivalence relation $R$ is reflexive and hence a partial order $R$ is reflexive and hence not an equivalence relation None of the above
Kathleen
asked
in
Set Theory & Algebra
Oct 8, 2014
by
Kathleen
14.3k
views
gate1995
set-theory&algebra
relations
normal
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