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Recent questions and answers in Mathematical Logic
4
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4
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1
Self Doubt: Mathematical Logic
Is the assertion "This statement is false" a proposition?
TusharRana
answered
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Mathematical Logic
1 day
ago
by
TusharRana
2.1k
views
mathematical-logic
6
votes
3
answers
2
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
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1-mark
3
votes
2
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3
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
4
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
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normal
0
votes
1
answer
5
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
67
views
propositional-logic
mathematical-logic
14
votes
8
answers
6
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
2
votes
3
answers
7
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
8
Why (p ∨ T) is not a tautology?
tbhaxor
answered
in
Mathematical Logic
Mar 6
by
tbhaxor
109
views
mathematical-logic
propositional-logic
87
votes
7
answers
9
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
89.8k
views
gatecse-2004
mathematical-logic
easy
isro2007
first-order-logic
0
votes
0
answers
10
#discrete
Çșȇ ʛấẗẻ
asked
in
Mathematical Logic
Feb 24
by
Çșȇ ʛấẗẻ
51
views
discrete-mathematics
kenneth-rosen
1
vote
1
answer
11
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
103
views
engineering-mathematics
propositional-logic
36
votes
6
answers
12
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
13
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
14
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
15
Permutation and combination
TusharRana
answered
in
Mathematical Logic
Feb 15
by
TusharRana
109
views
combinatory
engineering-mathematics
discrete-mathematics
1
vote
1
answer
16
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
172
views
gate2024-da-memory-based
goclasses
mathematical-logic
propositional-logic
100
votes
11
answers
17
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
19.6k
views
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mathematical-logic
normal
numerical-answers
propositional-logic
11
votes
2
answers
18
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
701
views
goclasses2024-mockgate-14
mathematical-logic
propositional-logic
multiple-selects
2-marks
0
votes
0
answers
19
Memory Based GATE DA 2024 | Question: 57
First-order logic question: All balls are round except rugby balls.
GO Classes
asked
in
Mathematical Logic
Feb 5
by
GO Classes
87
views
gate2024-da-memory-based
goclasses
mathematical-logic
first-order-logic
0
votes
0
answers
20
madeeasy
plz explain option c
nihal_chourasiya
asked
in
Mathematical Logic
Feb 1
by
nihal_chourasiya
85
views
engineering-mathematics
maxima-minima
0
votes
1
answer
21
Why inclusive or is used with Either...Or... here?
There are 2 propositions p: It is below freezing q: It is snowing. I want to write the symbolic form of: Either it is below freezing or it is snowing, but it is not snowing if it is freezing. This is what I came up with: ... . Second part it clear to me, but in the first shouldn't it will be exclusive or, because of Either...or...?
Mrityudoot
answered
in
Mathematical Logic
Jan 27
by
Mrityudoot
112
views
propositional-logic
10
votes
1
answer
22
GO Classes Test Series 2024 | Mock GATE | Test 12 | Question: 45
Below is a drawing(graph representation) of a binary relation $\text{R}$ over a set $\text{P}$ of elements $\{ \text{A, B, C, D, E, F}\}:$ Which of the following first-order logic statements about $\mathrm{R}$ ... $\forall x \in P . \exists y \in P . x R y$
GauravRajpurohit
answered
in
Mathematical Logic
Jan 21
by
GauravRajpurohit
550
views
goclasses2024-mockgate-12
goclasses
mathematical-logic
first-order-logic
multiple-selects
2-marks
1
vote
1
answer
23
cyclic group
1-) 1 2-) 2 3-) 3 4-) 4
Manukumr
answered
in
Mathematical Logic
Jan 21
by
Manukumr
437
views
group-theory
cyclic-
0
votes
0
answers
24
Madeeasy test 45, question 48
Can anyone please explain the statements II and III?
VinayBhojwani
asked
in
Mathematical Logic
Jan 16
by
VinayBhojwani
137
views
2-marks
engineering-mathematics
made-easy-test-series
50
votes
9
answers
25
GATE IT 2005 | Question: 36
Let $P(x)$ and $Q(x)$ ...
Acrizio
answered
in
Mathematical Logic
Jan 13
by
Acrizio
14.5k
views
gateit-2005
mathematical-logic
first-order-logic
normal
0
votes
2
answers
26
Confusion between implication with its converse.
I have given two propositions p: You drive over 65 mph q: You get a speeding ticket Here are two natural language statements Driving over 65 mph is sufficient for getting a speeding ticket (answer key: $p \to q$) Whenever you get a speeding ... , anything that comes after when/whenever is the antecedent, it should be $p \to q$. Where I am wrong here?
prasantkr.singh
answered
in
Mathematical Logic
Jan 12
by
prasantkr.singh
149
views
propositional-logic
0
votes
0
answers
27
Made Easy Mock Test 2
Rohit Chakraborty
asked
in
Mathematical Logic
Jan 11
by
Rohit Chakraborty
192
views
graph-theory
made-easy-test-series
engineering-mathematics
0
votes
0
answers
28
GATE 2021 | MATHS | QUESTION
Let $ \mathbb{F} $ be a finite field, and $ \mathbb{F}^{\times} $ be the group of all nonzero elements of $ \mathbb{F} $ under multiplication. If $ \mathbb{F}^{\times} $ has a subgroup of order $ 17 $, then the smallest possible order of the field $ \mathbb{F} $ is ____________________________
rajveer43
asked
in
Mathematical Logic
Jan 10
by
rajveer43
95
views
discrete-mathematics
0
votes
0
answers
29
GATE 2022 Stat | Question 16 | Linear Algebra
rajveer43
asked
in
Mathematical Logic
Jan 9
by
rajveer43
35
views
linear-algebra
1
vote
0
answers
30
GATE 2022 | Linear Algebra | Question 11
Let 𝑴 be a 2 × 2 real matrix such that $(𝑰 + 𝑴)^-1 = 𝑰 − 𝛼𝑴$, where 𝛼 is a non-zero real number and 𝑰 is the 2 × 2 identity matrix. If the trace of the matrix 𝑴 is 3, then the value of 𝛼 is (A) 3/4 (B) 1/3 (C) 1/2 (D) 1/4
rajveer43
asked
in
Mathematical Logic
Jan 9
by
rajveer43
73
views
linear-algebra
0
votes
1
answer
31
Generating Functions
yuyutsu
answered
in
Mathematical Logic
Jan 9
by
yuyutsu
198
views
discrete-mathematics
kenneth-rosen
generating-functions
22
votes
5
answers
32
GATE CSE 2023 | Question: 16
Geetha has a conjecture about integers, which is of the form \[ \forall x(P(x) \Longrightarrow \exists y Q(x, y)), \] where $P$ is a statement about integers, and $Q$ is a statement about pairs of integers. Which of the following (one or more) option(s) would imply ... $\exists y \forall x(P(x) \Longrightarrow Q(x, y))$ $\exists x(P(x) \wedge \exists y Q(x, y))$
whightspace
answered
in
Mathematical Logic
Jan 6
by
whightspace
10.9k
views
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first-order-logic
multiple-selects
1-mark
0
votes
1
answer
33
How to find continuity and Diffrentiability
The real function f(x) = cos (|x|) is
ButterChicken
answered
in
Mathematical Logic
Jan 6
by
ButterChicken
63
views
4
votes
5
answers
34
GO Classes Weekly Quiz 4 | Propositional Logic | Question: 6
If $(p \wedge \sim q) \wedge(p \wedge r) \rightarrow \sim p \vee q$ is false, then the truth values of $p, q$ and $r$ are, respectively : $F, T, F$ $T, F, T$ $T, T, T$ $F, F, F$
Sandip Das
answered
in
Mathematical Logic
Jan 3
by
Sandip Das
669
views
goclasses2024_wq4
goclasses
mathematical-logic
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1-mark
0
votes
1
answer
35
If |x| <1. Find the sum to infinity of the series 3 + 8x + 13x^2 + .......
If |x| < 1. Find the sum to infinity of the series $3 + 8x + 13x^2 + 18x^3 + ----- \infty$ $(3+2x)/(1-x^2)$ $(3-2x)/(1+x^2)$ $(2x-3)/(1-x^2)$ $(3+2x)/(1+x^2)$
gautham_reddy
answered
in
Mathematical Logic
Jan 1
by
gautham_reddy
316
views
0
votes
0
answers
36
Worksheet on Recurrence Relation
Find recurrence relations that are satisfied by the sequence formed from the following functions. (a) an = n!/15! (b) an = n2 − 6n + 8
Dagi
asked
in
Mathematical Logic
Jan 1
by
Dagi
104
views
0
votes
0
answers
37
#logic
Sir, In discrete mathematics 2024's lecture-17, at 15:30 you said "Every proposition variable is also a compound proposition". How it's possible Sir??? becoz by the definition of compound proposition, a proposition must contain a logical operator for being a compound proposition. @Deepak Poonia
pavan singh
asked
in
Mathematical Logic
Dec 30, 2023
by
pavan singh
121
views
goclasses
discrete-mathematics
propositional-logic
39
votes
9
answers
38
GATE CSE 1991 | Question: 03,xii
If $F_1$, $F_2$ and $F_3$ are propositional formulae such that $F_1 \land F_2 \rightarrow F_3$ and $F_1 \land F_2 \rightarrow \sim F_3$ are both tautologies, then which of the following is true: Both $F_1$ and $F_2$ are tautologies The conjunction $F_1 \land F_2$ is not satisfiable Neither is tautologous Neither is satisfiable None of the above
yuyutsu
answered
in
Mathematical Logic
Dec 29, 2023
by
yuyutsu
8.5k
views
gate1991
mathematical-logic
normal
propositional-logic
multiple-selects
0
votes
4
answers
39
Made Easy Probability - Let X be a set containing n elements. Three subsets A,B, C of X are chosen at random. The probability that A, B, C are pairwise disjoint is? (What do they mean by pairwise disjoint? and how should I approach this question?)
Nikhil_dhama
answered
in
Probability
Dec 28, 2023
by
Nikhil_dhama
934
views
probability
combinatory
counting
made-easy-test-series
gate-preparation
test-series
engineering-mathematics
self-doubt
bad-question
111
votes
6
answers
40
GATE CSE 2003 | Question: 33
Consider the following formula and its two interpretations \(I_1\) and \(I_2\). \(\alpha: (\forall x)\left[P_x \Leftrightarrow (\forall y)\left[Q_{xy} \Leftrightarrow \neg Q_{yy} \right]\right] \Rightarrow (\forall x)\left[\neg P_x\right]\) \(I_1\) : Domain: ... I_1\) does not Neither \(I_1\) nor \(I_2\) satisfies \(\alpha\) Both \(I_1\) and \(I_2\) satisfies \(\alpha\)
ssingla
answered
in
Mathematical Logic
Dec 28, 2023
by
ssingla
15.5k
views
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