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Recent questions and answers in Mathematical Logic
25
votes
4
answers
1
TIFR CSE 2010 | Part A | Question: 8
Which of the following is NOT necessarily true? { Notation: The symbol ''$\neg$''notes negation; $P (x, y)$ means that for given $x$ and $y$, the property $P(x, y)$ is true }. $(∀x∀y P(x, y)) \Rightarrow (∀y∀x P(x, y))$ ... $(∃x∀y P(x, y)) \Rightarrow (∀y∃x P(x, y))$ $(∀x∃y P(x, y)) \Rightarrow (∃y∀x P(x, y))$
Sahil5635
answered
in
Mathematical Logic
Mar 24
by
Sahil5635
3.3k
views
tifr2010
mathematical-logic
first-order-logic
0
votes
1
answer
2
Discrete mathematics Ch 1 : Propositional logic , Topic 2 : Logical operators or connectives
Which of the following is the negation of x is even iff x is divisible by 2 a) (x is even or x is not divisible by 2) and (x is not even or x is divisible by 2) b) (x is even and x is not divisible by 2) ... is divisible by 2) c) x is not even iff x is not divisible by 2 d) x is even if x is divisible by 2
KraVLonE
answered
in
Mathematical Logic
Mar 20
by
KraVLonE
60
views
42
votes
8
answers
3
GATE CSE 2020 | Question: 39
Which one of the following predicate formulae is NOT logically valid? Note that $W$ is a predicate formula without any free occurrence of $x$. $\forall x (p(x) \vee W) \equiv \forall x \: ( px) \vee W$ ... $\exists x(p(x) \rightarrow W) \equiv \forall x \: p(x) \rightarrow W$
Rohit139
answered
in
Mathematical Logic
Mar 20
by
Rohit139
17.0k
views
gatecse-2020
first-order-logic
mathematical-logic
2-marks
4
votes
4
answers
4
Self Doubt: Mathematical Logic
Is the assertion "This statement is false" a proposition?
TusharRana
answered
in
Mathematical Logic
Mar 18
by
TusharRana
2.1k
views
mathematical-logic
6
votes
3
answers
5
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
Mar 15
by
i_m_sudip
314
views
goclasses2024_wq5
goclasses
mathematical-logic
propositional-logic
1-mark
3
votes
2
answers
6
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
Mar 15
by
i_m_sudip
356
views
goclasses2024_wq5
goclasses
mathematical-logic
propositional-logic
multiple-selects
2-marks
34
votes
4
answers
7
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
Mar 13
by
i_m_sudip
6.5k
views
gatecse-2005
mathematical-logic
propositional-logic
normal
0
votes
1
answer
8
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 ... 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
Mar 12
by
I_M_CK
102
views
propositional-logic
mathematical-logic
14
votes
8
answers
9
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
8.1k
views
gatecse-2021-set1
mathematical-logic
propositional-logic
1-mark
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
3.0k
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
136
views
mathematical-logic
propositional-logic
87
votes
7
answers
12
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
110k
views
gatecse-2004
mathematical-logic
easy
isro2007
first-order-logic
0
votes
0
answers
13
#discrete
Çșȇ ʛấẗẻ
asked
in
Mathematical Logic
Feb 24
by
Çșȇ ʛấẗẻ
61
views
discrete-mathematics
kenneth-rosen
1
vote
1
answer
14
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
124
views
engineering-mathematics
propositional-logic
37
votes
6
answers
15
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
16
Regular expression to finite automata
Çșȇ ʛấẗẻ
asked
in
Mathematical Logic
Feb 15
by
Çșȇ ʛấẗẻ
199
views
finite-automata
theory-of-computation
regular-expression
0
votes
0
answers
17
COA Self doubt
Çșȇ ʛấẗẻ
asked
in
Mathematical Logic
Feb 15
by
Çșȇ ʛấẗẻ
87
views
co-and-architecture
self-doubt
0
votes
1
answer
18
Permutation and combination
TusharRana
answered
in
Mathematical Logic
Feb 15
by
TusharRana
124
views
combinatory
engineering-mathematics
discrete-mathematics
1
vote
1
answer
19
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
192
views
gate2024-da-memory-based
goclasses
mathematical-logic
propositional-logic
100
votes
11
answers
20
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
19.7k
views
gatecse-2016-set2
mathematical-logic
normal
numerical-answers
propositional-logic
11
votes
2
answers
21
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
752
views
goclasses2024-mockgate-14
mathematical-logic
propositional-logic
multiple-selects
2-marks
0
votes
0
answers
22
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 4
by
GO Classes
94
views
gate2024-da-memory-based
goclasses
mathematical-logic
first-order-logic
0
votes
0
answers
23
madeeasy
plz explain option c
nihal_chourasiya
asked
in
Mathematical Logic
Feb 1
by
nihal_chourasiya
92
views
engineering-mathematics
maxima-minima
0
votes
1
answer
24
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
126
views
propositional-logic
10
votes
1
answer
25
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
580
views
goclasses2024-mockgate-12
goclasses
mathematical-logic
first-order-logic
multiple-selects
2-marks
1
vote
1
answer
26
cyclic group
1-) 1 2-) 2 3-) 3 4-) 4
Manukumr
answered
in
Mathematical Logic
Jan 21
by
Manukumr
455
views
group-theory
cyclic-
0
votes
0
answers
27
Madeeasy test 45, question 48
Can anyone please explain the statements II and III?
VinayBhojwani
asked
in
Mathematical Logic
Jan 15
by
VinayBhojwani
144
views
2-marks
engineering-mathematics
made-easy-test-series
50
votes
9
answers
28
GATE IT 2005 | Question: 36
Let $P(x)$ and $Q(x)$ ...
Acrizio
answered
in
Mathematical Logic
Jan 13
by
Acrizio
14.7k
views
gateit-2005
mathematical-logic
first-order-logic
normal
0
votes
2
answers
29
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
172
views
propositional-logic
0
votes
0
answers
30
Made Easy Mock Test 2
Rohit Chakraborty
asked
in
Mathematical Logic
Jan 11
by
Rohit Chakraborty
225
views
graph-theory
made-easy-test-series
engineering-mathematics
0
votes
0
answers
31
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
105
views
discrete-mathematics
0
votes
0
answers
32
GATE 2022 Stat | Question 16 | Linear Algebra
rajveer43
asked
in
Mathematical Logic
Jan 9
by
rajveer43
41
views
linear-algebra
1
vote
0
answers
33
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
79
views
linear-algebra
0
votes
1
answer
34
Generating Functions
yuyutsu
answered
in
Mathematical Logic
Jan 8
by
yuyutsu
221
views
discrete-mathematics
kenneth-rosen
generating-functions
23
votes
5
answers
35
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
11.0k
views
gatecse-2023
mathematical-logic
first-order-logic
multiple-selects
1-mark
0
votes
1
answer
36
How to find continuity and Diffrentiability
The real function f(x) = cos (|x|) is
ButterChicken
answered
in
Mathematical Logic
Jan 5
by
ButterChicken
73
views
0
votes
1
answer
37
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
327
views
0
votes
0
answers
38
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
Dec 31, 2023
by
Dagi
110
views
0
votes
0
answers
39
#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
124
views
goclasses
discrete-mathematics
propositional-logic
39
votes
9
answers
40
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 28, 2023
by
yuyutsu
8.7k
views
gate1991
mathematical-logic
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