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Search results for mathematical-logic
40
votes
9
answers
41
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
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 ...
Kathleen
8.6k
views
Kathleen
asked
Sep 12, 2014
Mathematical Logic
gate1991
mathematical-logic
normal
propositional-logic
multiple-selects
+
–
11
votes
2
answers
42
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.
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...
GO Classes
727
views
GO Classes
asked
Feb 5
Mathematical Logic
goclasses2024-mockgate-14
mathematical-logic
propositional-logic
multiple-selects
2-marks
+
–
54
votes
6
answers
43
GATE CSE 2006 | Question: 26
Which one of the first order predicate calculus statements given below correctly expresses the following English statement? Tigers and lions attack if they are hungry or threatened. ...
Which one of the first order predicate calculus statements given below correctly expresses the following English statement? Tigers and lions attack if they are hungry or ...
Rucha Shelke
9.1k
views
Rucha Shelke
asked
Sep 18, 2014
Mathematical Logic
gatecse-2006
mathematical-logic
normal
first-order-logic
+
–
10
votes
1
answer
44
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 $\mathrm{R}$ ... $\forall x \in P . \exists y \in P . x R y$
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-ord...
GO Classes
578
views
GO Classes
asked
Jan 21
Mathematical Logic
goclasses2024-mockgate-12
goclasses
mathematical-logic
first-order-logic
multiple-selects
2-marks
+
–
43
votes
8
answers
45
GATE CSE 2007 | Question: 22
Let $\text{ Graph}(x)$ be a predicate which denotes that $x$ is a graph. Let $\text{ Connected}(x)$ be a predicate which denotes that $x$ ... $\forall x \, \Bigl ( \text{ Graph}(x) \implies \lnot \text{ Connected}(x) \Bigr )$
Let $\text{ Graph}(x)$ be a predicate which denotes that $x$ is a graph. Let $\text{ Connected}(x)$ be a predicate which denotes that $x$ is connected. Which of the follo...
Kathleen
8.8k
views
Kathleen
asked
Sep 21, 2014
Mathematical Logic
gatecse-2007
mathematical-logic
easy
first-order-logic
+
–
0
votes
1
answer
46
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.
Let's take a compound propositionsEither it is below freezing or it is snowing.Now if$p$: it is below freezing $q$: it is snowingWill it be $p \vee q$ or $p \oplus q$? Th...
tbhaxor
99
views
tbhaxor
asked
Mar 12
Mathematical Logic
propositional-logic
mathematical-logic
+
–
1
votes
1
answer
47
Why (p ∨ T) is not a tautology?
tbhaxor
139
views
tbhaxor
asked
Mar 5
Mathematical Logic
mathematical-logic
propositional-logic
+
–
33
votes
6
answers
48
GATE CSE 2015 Set 2 | Question: 3
Consider the following two statements. $S_1$: If a candidate is known to be corrupt, then he will not be elected $S_2$: If a candidate is kind, he will be elected Which one of the following statements follows from $S_1$ and $S_2$ as per sound inference ... If a person is kind, he is not known to be corrupt If a person is not kind, he is not known to be corrupt
Consider the following two statements.$S_1$: If a candidate is known to be corrupt, then he will not be elected$S_2$: If a candidate is kind, he will be electedWhich one ...
go_editor
8.7k
views
go_editor
asked
Feb 12, 2015
Mathematical Logic
gatecse-2015-set2
mathematical-logic
normal
logical-reasoning
+
–
33
votes
5
answers
49
GATE CSE 2012 | Question: 1
Consider the following logical inferences. $I_{1}$: If it rains then the cricket match will not be played. The cricket match was played. Inference: There was no rain. $I_{2}$: If it rains then the cricket match will not be played. It did not rain. Inference: ... $I_{2}$ is a correct inference Both $I_{1}$ and $I_{2}$ are not correct inferences
Consider the following logical inferences.$I_{1}$: If it rains then the cricket match will not be played.The cricket match was played.Inference: There was no rain.$I_{2}...
gatecse
9.0k
views
gatecse
asked
Aug 5, 2014
Mathematical Logic
gatecse-2012
mathematical-logic
easy
logical-reasoning
+
–
1
votes
1
answer
50
Memory Based GATE DA 2024 | Question: 33
Which of the following are tautologies? \(x \land \neg y \Rightarrow y \rightarrow x\) \(\neg x \land y \Rightarrow \neg x \rightarrow y\) \(x \land \neg y \Rightarrow \neg x \rightarrow y\) \(\neg x \land y \Rightarrow y \rightarrow x\)
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 \ne...
GO Classes
191
views
GO Classes
asked
Feb 4
Mathematical Logic
gate2024-da-memory-based
goclasses
mathematical-logic
propositional-logic
+
–
40
votes
8
answers
51
GATE CSE 2009 | Question: 23
Which one of the following is the most appropriate logical formula to represent the statement? "Gold and silver ornaments are precious". The following notations are used: $G(x): x$ is a gold ornament $S(x): x$ is a silver ornament $P(x): x$ ... $\forall x((G(x) \vee S(x)) \implies P(x))$
Which one of the following is the most appropriate logical formula to represent the statement?"Gold and silver ornaments are precious".The following notations are used: ...
gatecse
8.3k
views
gatecse
asked
Sep 15, 2014
Mathematical Logic
gatecse-2009
mathematical-logic
easy
first-order-logic
+
–
41
votes
4
answers
52
GATE CSE 1995 | Question: 2.19
If the proposition $\lnot p \to q$ is true, then the truth value of the proposition $\lnot p \lor \left ( p \to q \right )$, where $\lnot$ is negation, $\lor$ is inclusive OR and $\to$ is implication, is True Multiple Values False Cannot be determined
If the proposition $\lnot p \to q$ is true, then the truth value of the proposition $\lnot p \lor \left ( p \to q \right )$, where $\lnot$ is negation, $\lor$ is inclusiv...
Kathleen
8.5k
views
Kathleen
asked
Oct 8, 2014
Mathematical Logic
gate1995
mathematical-logic
normal
propositional-logic
+
–
0
votes
0
answers
53
Memory Based GATE DA 2024 | Question: 57
First-order logic question: All balls are round except rugby balls.
First-order logic question: All balls are round except rugby balls.
GO Classes
97
views
GO Classes
asked
Feb 4
Mathematical Logic
gate2024-da-memory-based
goclasses
mathematical-logic
first-order-logic
+
–
30
votes
5
answers
54
GATE CSE 2001 | Question: 1.3
Consider two well-formed formulas in propositional logic $F_1: P \Rightarrow \neg P$ $F_2: (P \Rightarrow \neg P) \lor ( \neg P \Rightarrow P)$ Which one of the following statements is correct? $F_1$ is satisfiable, $F_2$ is valid $F_1$ unsatisfiable, $F_2$ is satisfiable $F_1$ is unsatisfiable, $F_2$ is valid $F_1$ and $F_2$ are both satisfiable
Consider two well-formed formulas in propositional logic$F_1: P \Rightarrow \neg P$ $F_2: (P \Rightarrow \neg P) \lor ( \neg P \Rightarrow P)$Which one of the fo...
Kathleen
8.9k
views
Kathleen
asked
Sep 14, 2014
Mathematical Logic
gatecse-2001
mathematical-logic
easy
propositional-logic
+
–
33
votes
4
answers
55
GATE CSE 2012 | Question: 13
What is the correct translation of the following statement into mathematical logic? “Some real numbers are rational” $\exists x (\text{real}(x) \lor \text{rational}(x))$ $\forall x (\text{real}(x) \to \text{rational}(x))$ $\exists x (\text{real}(x) \wedge \text{rational}(x))$ $\exists x (\text{rational}(x) \to \text{real}(x))$
What is the correct translation of the following statement into mathematical logic?“Some real numbers are rational”$\exists x (\text{real}(x) \lor \text{rational}(x))...
gatecse
8.5k
views
gatecse
asked
Aug 5, 2014
Mathematical Logic
gatecse-2012
mathematical-logic
easy
first-order-logic
+
–
1
votes
0
answers
56
Mathematical Logic: Which of the following is a logical consequence of $∀x(p(x)∨q(x))$
The following question is on the NPTEL archive of Assignment 2 of Discrete Mathematics Course,(Link : assessment id-15 (nptel.ac.in)) . I am not able to get how the answer is given option A but I am getting B, C and D. I have also attached my reasoning below. Let me know If I am missing something.
The following question is on the NPTEL archive of Assignment 2 of Discrete Mathematics Course,(Link : assessment id-15 (nptel.ac.in)) . I am not able to get howthe answe...
USharma02
204
views
USharma02
asked
Dec 24, 2023
Mathematical Logic
mathematical-logic
first-order-logic
discrete-mathematics
+
–
33
votes
8
answers
57
GATE CSE 2009 | Question: 24
The binary operation $\Box$ ... following is equivalent to $P \vee Q$? $\neg Q \Box \neg P$ $P\Box \neg Q$ $\neg P\Box Q$ $\neg P\Box \neg Q$
The binary operation $\Box$ is defined as follows$$\begin{array}{|c|c|c|} \hline \textbf{P} & \textbf{Q} & \textbf{P} \Box \textbf{Q}\\\hline \text{T} & \text{T}& \text{T...
gatecse
8.4k
views
gatecse
asked
Sep 15, 2014
Mathematical Logic
gatecse-2009
mathematical-logic
easy
propositional-logic
+
–
37
votes
11
answers
58
GATE CSE 2014 Set 3 | Question: 53
The CORRECT formula for the sentence, "not all Rainy days are Cold" is $\forall d (\text{Rainy}(d) \wedge \text{~Cold}(d))$ $\forall d ( \text{~Rainy}(d) \to \text{Cold}(d))$ $\exists d(\text{~Rainy}(d) \to \text{Cold}(d))$ $\exists d(\text{Rainy}(d) \wedge \text{~Cold}(d))$
The CORRECT formula for the sentence, "not all Rainy days are Cold" is$\forall d (\text{Rainy}(d) \wedge \text{~Cold}(d))$$\forall d ( \text{~Rainy}(d) \to \text{Cold}(d)...
go_editor
7.7k
views
go_editor
asked
Sep 28, 2014
Mathematical Logic
gatecse-2014-set3
mathematical-logic
easy
first-order-logic
+
–
30
votes
7
answers
59
GATE CSE 2008 | Question: 31
$P$ and $Q$ are two propositions. Which of the following logical expressions are equivalent? $P ∨ \neg Q$ $\neg(\neg P ∧ Q)$ $(P ∧ Q) ∨ (P ∧ \neg Q) ∨ (\neg P ∧ \neg Q)$ $(P ∧ Q) ∨ (P ∧ \neg Q) ∨ (\neg P ∧ Q)$ Only I and II Only I, II and III Only I, II and IV All of I, II, III and IV
$P$ and $Q$ are two propositions. Which of the following logical expressions are equivalent?$P ∨ \neg Q$$\neg(\neg P ∧ Q)$$(P ∧ Q) ∨ (P ∧ \neg Q) ∨ (\neg P �...
Kathleen
8.3k
views
Kathleen
asked
Sep 12, 2014
Mathematical Logic
gatecse-2008
normal
mathematical-logic
propositional-logic
+
–
37
votes
6
answers
60
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 $x$ ... $\exists x: \text{glitters}(x)\wedge \neg \text{gold}(x)$
Consider the statement "Not all that glitters is gold”Predicate glitters$(x)$ is true if $x$ glitters and predicate gold$(x)$ is true if $x$ is gold. Which one of the ...
gatecse
6.5k
views
gatecse
asked
Sep 15, 2014
Mathematical Logic
gatecse-2014-set1
mathematical-logic
first-order-logic
+
–
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