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Recent questions and answers in Discrete Mathematics
4
votes
4
answers
1
Self Doubt: Mathematical Logic
Is the assertion "This statement is false" a proposition?
TusharRana
answered
in
Mathematical Logic
23 hours
ago
by
TusharRana
2.1k
views
mathematical-logic
36
votes
6
answers
2
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 ______
ritiksri8
answered
in
Set Theory & Algebra
1 day
ago
by
ritiksri8
11.6k
views
gatecse-2017-set2
set-theory&algebra
lattice
numerical-answers
normal
6
votes
3
answers
3
GO Classes Weekly Quiz 5 | Propositional Logic | Question: 2
Which of the following expressions is false? $p \rightarrow q \equiv q \rightarrow p$ $\neg(p \vee q) \equiv \neg p \wedge \neg q$ $p \rightarrow q \equiv \neg q \rightarrow \neg p$ none of the above
i_m_sudip
answered
in
Mathematical Logic
4 days
ago
by
i_m_sudip
290
views
goclasses2024_wq5
goclasses
mathematical-logic
propositional-logic
1-mark
3
votes
2
answers
4
GO Classes Weekly Quiz 5 | Propositional Logic | Question: 13
Let $p,q,r$ be three propositional variables. Which of the following statements is/are false? $p \rightarrow(q \vee r)) \equiv((p \wedge \neg q) \rightarrow r)$ $(p \wedge q) \vee r \equiv p \wedge(q \vee r)$ ... is FALSE then $(q \rightarrow p)$ is TRUE. If $(p \rightarrow q)$ is TRUE then $(q \rightarrow p)$ is FALSE.
i_m_sudip
answered
in
Mathematical Logic
4 days
ago
by
i_m_sudip
332
views
goclasses2024_wq5
goclasses
mathematical-logic
propositional-logic
multiple-selects
2-marks
34
votes
4
answers
5
GATE CSE 2005 | Question: 40
Let $P, Q,$ and $R$ be three atomic propositional assertions. Let $X$ denote $( P ∨ Q ) → R$ and $Y$ denote $(P → R) ∨ (Q → R).$ Which one of the following is a tautology? $X ≡ Y$ $X → Y$ $Y → X$ $¬Y → X$
i_m_sudip
answered
in
Mathematical Logic
5 days
ago
by
i_m_sudip
6.4k
views
gatecse-2005
mathematical-logic
propositional-logic
normal
0
votes
2
answers
6
Find no of sets A and B such that A n B = {3,5} and A U B = {2,3,5,7,8)
I_M_CK
answered
in
Set Theory & Algebra
5 days
ago
by
I_M_CK
63
views
0
votes
1
answer
7
Does Either...Or means Exclusive Or or Inclusive Or?
Let's take a compound propositions Either it is below freezing or it is snowing. Now if $p$: it is below freezing $q$: it is snowing Will it be $p \vee q$ or $p \oplus q$? There are some instances where semantics are required. For ... this both cases can't be true, because if you are ill you can't appear for example and you must be in one state.
I_M_CK
answered
in
Mathematical Logic
6 days
ago
by
I_M_CK
66
views
propositional-logic
mathematical-logic
14
votes
8
answers
8
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
ritiksri8
answered
in
Mathematical Logic
Mar 9
by
ritiksri8
8.0k
views
gatecse-2021-set1
mathematical-logic
propositional-logic
1-mark
24
votes
6
answers
9
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
ritiksri8
answered
in
Set Theory & Algebra
Mar 9
by
ritiksri8
16.1k
views
gate1995
set-theory&algebra
normal
set-theory
2
votes
3
answers
10
GATE CSE 2024 | Set 2 | Question: 2
Let $p$ and $q$ be the following propositions: $p$ : Fail grade can be given. $q$ : Student scores more than $50 \%$ marks. Consider the statement: "Fail grade cannot be given when student scores more than $50 \%$ marks." ... above statement in propositional logic? $q \rightarrow \neg p$ $q \rightarrow p$ $p \rightarrow q$ $\neg p \rightarrow q$
Rohit139
answered
in
Mathematical Logic
Mar 6
by
Rohit139
2.8k
views
gatecse2024-set2
mathematical-logic
1
vote
1
answer
11
Why (p ∨ T) is not a tautology?
tbhaxor
answered
in
Mathematical Logic
Mar 6
by
tbhaxor
108
views
mathematical-logic
propositional-logic
0
votes
2
answers
12
Kenneth Rosen Edition 7 Exercise 6.1 Question 57 (Page No. 398)
The name of a variable in the JAVA programming language is a string of between $1$ and $65,535$ characters, inclusive, where each character can be an uppercase or a lowercase letter, a dollar sign, an underscore, or a digit, except that the first character must not be a digit. Determine the number of different variable names in JAVA.
Shriram BM
answered
in
Combinatory
Mar 4
by
Shriram BM
1.1k
views
kenneth-rosen
discrete-mathematics
counting
descriptive
87
votes
7
answers
13
GATE CSE 2004 | Question: 23, ISRO2007-32
Identify the correct translation into logical notation of the following assertion. Some boys in the class are taller than all the girls Note: $\text{taller} (x, y)$ is true if $x$ is taller than $y$ ... $(\exists x) (\text{boy}(x) \land (\forall y) (\text{girl}(y) \rightarrow \text{taller}(x, y)))$
ritiksri8
answered
in
Mathematical Logic
Mar 3
by
ritiksri8
88.9k
views
gatecse-2004
mathematical-logic
easy
isro2007
first-order-logic
20
votes
5
answers
14
TIFR CSE 2016 | Part A | Question: 8
Let $A$ and $B$ be finite sets such that $A \subseteq B$. Then, what is the value of the expression: $ \sum \limits_{C:A \subseteq C \subseteq B} (-1)^{\mid C \setminus A \mid,}$ Where $C \setminus A=\{x \in C : x \notin A \}$? Always $0$ Always $1$ $0$ if $A=B$ and $1$ otherwise $1$ if $A=B$ and $0$ otherwise Depends on the size of the universe
Priyam Garg
answered
in
Set Theory & Algebra
Feb 28
by
Priyam Garg
2.6k
views
tifr2016
set-theory&algebra
set-theory
7
votes
4
answers
15
GATE CSE 2023 | Question: 5
The Lucas sequence $L_{n}$ is defined by the recurrence relation: \[ L_{n}=L_{n-1}+L_{n-2}, \quad \text { for } \quad n \geq 3, \] with $L_{1}=1$ and $L_{2}=3$ ... $L_{n}=\left(\frac{1+\sqrt{5}}{2}\right)^{n}-\left(\frac{1-\sqrt{5}}{2}\right)^{n}$
Priyam Garg
answered
in
Combinatory
Feb 28
by
Priyam Garg
7.7k
views
gatecse-2023
combinatory
recurrence-relation
1-mark
19
votes
18
answers
16
GATE CSE 2019 | Question: 21
The value of $3^{51} \text{ mod } 5$ is _____
ravi2002
answered
in
Combinatory
Feb 26
by
ravi2002
17.9k
views
gatecse-2019
numerical-answers
combinatory
modular-arithmetic
1-mark
0
votes
0
answers
17
#discrete
Çșȇ ʛấẗẻ
asked
in
Mathematical Logic
Feb 24
by
Çșȇ ʛấẗẻ
51
views
discrete-mathematics
kenneth-rosen
0
votes
0
answers
18
Question on Quotient set
What will be quotient set for equivalence relation R={(x,y) ∣ x ≡ y mod 5} in set builder form?
rick55
asked
in
Set Theory & Algebra
Feb 24
by
rick55
44
views
2
votes
2
answers
19
GATE CSE 2024 | Set 2 | Question: 53
Let $Z_{n}$ be the group of integers $\{0,1,2, \ldots, n-1\}$ with addition modulo $n$ as the group operation. The number of elements in the group $Z_{2} \times Z_{3} \times Z_{4}$ that are their own inverses is ___________.
amit166
answered
in
Set Theory & Algebra
Feb 22
by
amit166
1.7k
views
gatecse2024-set2
numerical-answers
set-theory&algebra
group-theory
1
vote
2
answers
20
GATE CSE 2024 | Set 2 | Question: 24
Let $\text{P}$ be the partial order defined on the set $\{1,2,3,4\}$ as follows \[ P=\{(x, x) \mid x \in\{1,2,3,4\}\} \cup\{(1,2),(3,2),(3,4)\} \] The number of total orders on $\{1,2,3,4\}$ that contain $\text{P}$ is __________.
amit166
answered
in
Set Theory & Algebra
Feb 22
by
amit166
1.7k
views
gatecse2024-set2
numerical-answers
set-theory&algebra
partial-order
0
votes
1
answer
21
DISCRETE
Let T be a tree with n vertices and k be the maximum size of an independent set in T. Then the size of maximum matching in T is (A) k (B) n−k (C) (n−1)/2
ks824
answered
in
Graph Theory
Feb 22
by
ks824
443
views
graph-matching
1
vote
1
answer
22
if p implies q is true then the truth value of which of the following cannot be determined
a) ~p\/q b) ~q=>~p c) ~p=>~q d) ~(p/\~q) can someone provide the solution?
TusharRana
answered
in
Mathematical Logic
Feb 21
by
TusharRana
102
views
engineering-mathematics
propositional-logic
2
votes
4
answers
23
ACE Test Series: Generating Function
The generating function of the sequence $\left \{ a_{0},a_{1},a_{2}..........a_{n}………...\infty \right \}$ where $a_{n}=\left ( n+2 \right )\left ( n+1 \right ).3^{n}$ is $a)3\left ( 1+3x \right )^{-2}$ $b)3\left ( 1-3x \right )^{-2}$ $c)2\left ( 1+3x \right )^{-3}$ $d)2\left ( 1-3x \right )^{-3}$
Priyam Garg
answered
in
Combinatory
Feb 20
by
Priyam Garg
1.5k
views
generating-functions
discrete-mathematics
24
votes
6
answers
24
TIFR CSE 2012 | Part A | Question: 7
It is required to divide the $2n$ members of a club into $n$ disjoint teams of $2$ members each. The teams are not labelled. The number of ways in which this can be done is: $\frac{\left ( 2n \right )!}{2^{n}}$ $\frac{\left ( 2n \right )!}{n!}$ $\frac{\left ( 2n \right )!}{2^n . n!}$ $\frac{n!}{2}$ None of the above
Priyam Garg
answered
in
Combinatory
Feb 18
by
Priyam Garg
4.5k
views
tifr2012
combinatory
balls-in-bins
0
votes
1
answer
25
GATE CSE 2024 | Set 1 | Question: 41
The chromatic number of a graph is the minimum number of colours used in a proper colouring of the graph. Let $G$ be any graph with $n$ vertices and chromatic number $k$. Which of the following statements is/are always TRUE? $G$ contains a complete subgraph with ... $n/k$ $G$ contains at least $k(k-1) / 2$ edges $G$ contains a vertex of degree at least $k$
minip
answered
in
Graph Theory
Feb 17
by
minip
1.7k
views
gatecse2024-set1
multiple-selects
graph-theory
1
vote
1
answer
26
GATE CSE 2024 | Set 1 | Question: 42
Consider the operators $\diamond$ and $\square$ defined by $a \diamond b=a+2 b, a \square b=a b$, for positive integers. Which of the following statements is/are TRUE? Operator $\diamond$ ... $\square$ obeys the distributive law Operator $\square$ over the operator $\diamond$ obeys the distributive law
shishir__roy
answered
in
Set Theory & Algebra
Feb 17
by
shishir__roy
1.6k
views
gatecse2024-set1
multiple-selects
set-theory&algebra
1
vote
2
answers
27
GATE CSE 2024 | Set 2 | Question: 50
The chromatic number of a graph is the minimum number of colours used in a proper colouring of the graph. The chromatic number of the following graph is __________.
Deepak Poonia
answered
in
Graph Theory
Feb 17
by
Deepak Poonia
1.6k
views
gatecse2024-set2
graph-theory
numerical-answers
2
votes
2
answers
28
GATE CSE 2024 | Set 2 | Question: 7
Let $\text{A}$ be the adjacency matrix of a simple undirected graph $\text{G}$. Suppose $\text{A}$ is its own inverse. Which one of the following statements is always TRUE? $\text{G}$ is a cycle $\text{G}$ is a perfect matching $\text{G}$ is a complete graph There is no such graph $\text{G}$
ankitgupta.1729
answered
in
Graph Theory
Feb 17
by
ankitgupta.1729
2.4k
views
gatecse2024-set2
graph-theory
0
votes
1
answer
29
GATE CSE 2024 | Set 1 | Question: 22
Let $A$ and $B$ be non-empty finite sets such that there exist one-to-one and onto functions $\text{(i)}$ from $A$ to $B$ and $\text{(ii)}$ from $A \times A$ to $A \cup B$. The number of possible values of $\text{|A|}$ is ___________.
shishir__roy
answered
in
Set Theory & Algebra
Feb 17
by
shishir__roy
1.5k
views
gatecse2024-set1
numerical-answers
set-theory&algebra
36
votes
6
answers
30
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 $x$ ... $\exists x: \text{glitters}(x)\wedge \neg \text{gold}(x)$
Discovery
answered
in
Mathematical Logic
Feb 16
by
Discovery
6.5k
views
gatecse-2014-set1
mathematical-logic
first-order-logic
0
votes
0
answers
31
Regular expression to finite automata
Çșȇ ʛấẗẻ
asked
in
Mathematical Logic
Feb 15
by
Çșȇ ʛấẗẻ
187
views
finite-automata
theory-of-computation
regular-expression
0
votes
0
answers
32
COA Self doubt
Çșȇ ʛấẗẻ
asked
in
Mathematical Logic
Feb 15
by
Çșȇ ʛấẗẻ
76
views
co-and-architecture
self-doubt
0
votes
1
answer
33
Permutation and combination
TusharRana
answered
in
Mathematical Logic
Feb 15
by
TusharRana
109
views
combinatory
engineering-mathematics
discrete-mathematics
0
votes
2
answers
34
Kenneth Rosen Edition 7 Exercise 6.3 Question 26 (Page No. 414)
Thirteen people on a softball team show up for a game. How many ways are there to choose $10$ players to take the field? How many ways are there to assign the $10$ positions by selecting players from the $13$ people who show ... ways are there to choose $10$ players to take the field if at least one of these players must be a woman?
Priyam Garg
answered
in
Combinatory
Feb 11
by
Priyam Garg
4.4k
views
kenneth-rosen
discrete-mathematics
counting
combinatory
descriptive
1
vote
1
answer
35
Memory Based GATE DA 2024 | Question: 33
Which of the following are tautologies? \(x \land \neg y \Rightarrow y \rightarrow x\) \(\neg x \land y \Rightarrow \neg x \rightarrow y\) \(x \land \neg y \Rightarrow \neg x \rightarrow y\) \(\neg x \land y \Rightarrow y \rightarrow x\)
pankaj kumar 70m
answered
in
Mathematical Logic
Feb 8
by
pankaj kumar 70m
171
views
gate2024-da-memory-based
goclasses
mathematical-logic
propositional-logic
1
vote
0
answers
36
Gate 2016
The minimum number of colours that is sufficient to vertex-colour any planar graph is ________. I am confused with the question's language. please correct me if I have a wrong assumption. We need to tell the minimum colors required for a planar graph. Suppose I start with ... is only fixed to 4. I understand the answer not to be less than 4. What does the word "any" means here?
TusharRana
asked
in
Graph Theory
Feb 8
by
TusharRana
170
views
100
votes
11
answers
37
GATE CSE 2016 Set 2 | Question: 01
Consider the following expressions: $false$ $Q$ $true$ $P\vee Q$ $\neg Q\vee P$ The number of expressions given above that are logically implied by $P \wedge (P \Rightarrow Q)$ is ___________.
TusharRana
answered
in
Mathematical Logic
Feb 8
by
TusharRana
19.5k
views
gatecse-2016-set2
mathematical-logic
normal
numerical-answers
propositional-logic
11
votes
2
answers
38
GO Classes Test Series 2024 | Mock GATE | Test 14 | Question: 58
Let $\mathrm{F}$ and $\mathrm{G}$ be two propositional formulae. Which of the following is/are True? If $F \vee G$ is a tautology then at least one of $F, G$ is a tautology. If $F \wedge G$ is a contradiction then at ... $G$ is a tautology. If $F \rightarrow G$ is a contradiction then $F$ is a tautology and $G$ is a contradiction.
Ayush Kumar_1
answered
in
Mathematical Logic
Feb 8
by
Ayush Kumar_1
700
views
goclasses2024-mockgate-14
mathematical-logic
propositional-logic
multiple-selects
2-marks
0
votes
0
answers
39
Combinatorics & Probability
A rumor is spread randomly among a group of 10 people by successively having one person call someone, who calls someone, and so on. A person can pass the rumor on to anyone except the individual who just called. (a) By how many different paths can a rumor ... in $N$ calls? (c) What is the probability that if $A$ starts the rumor, then $A$ receives the third calls?
Debargha Mitra Roy
asked
in
Combinatory
Feb 8
by
Debargha Mitra Roy
126
views
combinatory
counting
24
votes
4
answers
40
GATE CSE 1987 | Question: 9a
How many binary relations are there on a set $A$ with $n$ elements?
ssingla
answered
in
Set Theory & Algebra
Feb 7
by
ssingla
5.8k
views
gate1987
set-theory&algebra
relations
descriptive
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