Search results for propositional-logic / GATE Overflow for GATE CSE

41 votes

9 answers

21

GATE IT 2004 | Question: 31
Let $p, q, r$ and $s$ be four primitive statements. Consider the following arguments: $P: [(¬p\vee q) ∧ (r → s) ∧ (p \vee r)] → (¬s → q)$ $Q: [(¬p ∧q) ∧ [q → (p → r)]] → ¬r$ $R: [[(q ∧ r) → p] ∧ (¬q \vee p)] → r$ $S: [p ∧ (p → r) ∧ (q \vee ¬ r)] → q$ Which of the above arguments are valid? $P$ and $Q$ only $P$ and $R$ only $P$ and $S$ only $P, Q, R$ and $S$

Let $p, q, r$ and $s$ be four primitive statements. Consider the following arguments:$P: [(¬p\vee q) ∧ (r → s) ∧ (p \vee r)] → (¬s → q)$$Q: [(¬p ∧q) �...

Ishrat Jahan

11.9k views

Ishrat Jahan asked Nov 2, 2014

36 votes

3 answers

22

GO Classes CS 2025 | Weekly Quiz 2 | Propositional Logic | Question: 8
Let $\varphi$ be a propositional formula on a set of variables $A$ and $\psi$ be a propositional formula on a set of variables $B$ , such that $\varphi$ $\Rightarrow$ $\psi$ . A $\textit{Craig interpolant}$ of $\varphi$ and $\psi$ ... interpolant for $\varphi$ and $\psi?$ $\varphi$ itself $q \vee s$ $q \vee r$ $\neg q \wedge s$

Let $\varphi$ be a propositional formula on a set of variables $A$ and $\psi$ be a propositional formula on a set of variables $B$ , such that $\varphi$ $\Rightarrow$...

GO Classes

782 views

GO Classes asked Mar 26, 2023

58 votes

6 answers

23

GO Classes CS 2025 | Weekly Quiz 2 | Propositional Logic | Question: 16
If $\text{F1, F2}$ and $\text{F3}$ are propositional formulae/expressions, over some set of propositional variables, such that $\mathrm{F} 1 \vee F 2 \rightarrow \mathrm{F} 3$ is a contradiction, then which of the following is/ ... is a tautology. $\text{F3}$ is a contradiction. $\text{F1} \mathrm{v} \text{F2}$ is a tautology.

If $\text{F1, F2}$ and $\text{F3}$ are propositional formulae/expressions, over some set of propositional variables, such that $\mathrm{F} 1 \vee F 2 \rightarrow \mathrm{...

GO Classes

1.7k views

GO Classes asked Mar 26, 2023

12 votes

3 answers

24

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

854 views

GO Classes asked Feb 5

26 votes

6 answers

25

GO Classes CS 2025 | Weekly Quiz 1 | Propositional Logic | Question: 15
Consider the following popular puzzle. A boy and a girl are talking. One of them has black hair, another has white hair. I am a boy said the child with black hair. I am a girl said the child with white hair ... Which of them is lying? The boy only The girl only Both of them Information is not sufficient to find out the liar

Consider the following popular puzzle.A boy and a girl are talking. One of them has black hair, another has white hair.“I am a boy” said the child with black hair.“...

GO Classes

1.6k views

GO Classes asked Mar 30, 2022

21 votes

6 answers

26

GO Classes CS 2025 | Weekly Quiz 3 | Propositional Logic | Question: 9
Which of the following statements is/are true? The argument form with premises $p_1, p_2, \ldots, p_n$ and conclusion $q \rightarrow r$ is valid iff the argument form with premises $p_1, p_2, \ldots, p_n, r$ ... the argument form with premises $p_1, p_2, \ldots, p_n, \sim r$, and conclusion $\sim q$ is valid.

Which of the following statements is/are true?The argument form with premises $p_1, p_2, \ldots, p_n$ and conclusion $q \rightarrow r$ is valid iff the argument form with...

GO Classes

927 views

GO Classes asked Apr 5, 2023

40 votes

9 answers

27

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

9.0k views

Kathleen asked Sep 12, 2014

14 votes

3 answers

28

GO Classes CS 2025 | Weekly Quiz 1 | Propositional Logic | Question: 10
Given the truth table of a Binary Operation \$ as follows: $ ... }$ Identify the matching Boolean Expression. $X \$ \neg Y$ $\neg X \$ Y$ $\neg X \$ \neg Y$ none of the options

Given the truth table of a Binary Operation \$ as follows:$$\begin{array}{|l|l|l|l|} \hline {} \text{X} & \text{Y }& \text{X\$Y }\\ \hline \text{1} & \text{0 }& ...

GO Classes

1.1k views

GO Classes asked Dec 5, 2022

6 votes

2 answers

29

GO Classes CS 2025 | Weekly Quiz 3 | Propositional Logic | Question: 5
Which of the following compound propositions is/are a tautology? $[p \land (p \rightarrow q)] \rightarrow q$ $[q \land (p \rightarrow q)] \rightarrow p$ $[(p \lor q) \land (r \rightarrow p) \land (r \rightarrow q)] \rightarrow r$ $[(p \lor q) \land (p \rightarrow r) \land (q \rightarrow r)] \rightarrow r$

Which of the following compound propositions is/are a tautology?$[p \land (p \rightarrow q)] \rightarrow q$$[q \land (p \rightarrow q)] \rightarrow p$$[(p \lor q) \land (...

GO Classes

132 views

GO Classes asked Mar 29

10 votes

6 answers

30

GO Classes CS 2025 | Weekly Quiz 3 | Propositional Logic | Question: 3
Consider the following atomic propositions: $\text{R}$: It is Raining $\text{S}$ ... , and vice versa It is raining is equivalent to sonu is sick It is raining or sonu is sick but not both

Consider the following atomic propositions:$\text{R}$: It is Raining$\text{S}$: Sonu is SickWhich of the following is/are correct English Translation of the following log...

GO Classes

690 views

GO Classes asked Apr 5, 2023

1 votes

2 answers

31

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

183 views

tbhaxor asked Mar 12

2 votes

2 answers

32

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

256 views

GO Classes asked Feb 4

12 votes

2 answers

33

GO Classes CS 2025 | Weekly Quiz 3 | Propositional Logic | Question: 8
The Logic Problem, taken from $\text{"WFF'N PROOF, The Game of Logic"}$ has these two assumptions: "Logic is difficult or not many students like logic." "If mathematics is easy, then logic ... is not easy or logic is difficult." "Logic is not difficult or mathematics is not easy."

The Logic Problem, taken from $\text{"WFF'N PROOF, The Game of Logic"}$ has these two assumptions:"Logic is difficult or not many students like logic.""If mathematics is ...

GO Classes

460 views

GO Classes asked Apr 5, 2023

7 votes

2 answers

34

GO Classes CS 2025 | Weekly Quiz 3 | Propositional Logic | Question: 10
Let $F$ and $G$ be two propositional formula. Which of the following is/are True? $F \vee G$ is a tautology iff at least one of them is a tautology If $F \rightarrow G$ is a tautology and $F$ ... is a tautology. $(F \rightarrow G) \wedge (F \rightarrow \neg G)$ is a tautology iff $F$ is a contradiction.

Let $F$ and $G$ be two propositional formula.Which of the following is/are True?$F \vee G$ is a tautology iff at least one of them is a tautologyIf $F \rightarrow G$ is a...

GO Classes

737 views

GO Classes asked Apr 5, 2023

9 votes

5 answers

35

GO Classes CS 2025 | Weekly Quiz 1 | Propositional Logic | Question: 2
A sufficient condition for a triangle $T$ be a right triangle is that $a^2+b^2=c^2$. An equivalent statement is If $T$ is a right triangle then $a^2+b^2=c^2$. If $a^2+b^2=c^2$ then $T$ is a right triangle. If $a^2+b^2\neq c^2$ then $T$ is not a right triangle. $T$ is a right triangle only if $a^2+b^2=c^2$.

A sufficient condition for a triangle $T$ be a right triangle is that $a^2+b^2=c^2$. An equivalent statement isIf $T$ is a right triangle then $a^2+b^2=c^2$.If $a^2+b^2=c...

GO Classes

1.5k views

GO Classes asked Mar 23, 2022

45 votes

3 answers

36

GATE CSE 2006 | Question: 27
Consider the following propositional statements: $P_1: ((A ∧ B) → C)) ≡ ((A → C) ∧ (B → C))$ $P_2: ((A ∨ B) → C)) ≡ ((A → C) ∨ (B → C))$ Which one of the following is true? $P_1$ is a tautology, but not $P_2$ $P_2$ is a tautology, but not $P_1$ $P_1$ and $P_2$ are both tautologies Both $P_1$ and $P_2$ are not tautologies

Consider the following propositional statements:$P_1: ((A ∧ B) → C)) ≡ ((A → C) ∧ (B → C))$$P_2: ((A ∨ B) → C)) ≡ ((A → C) ∨ (B → C))$Which one of...

Rucha Shelke

8.6k views

Rucha Shelke asked Sep 18, 2014

1 votes

1 answer

37

Why (p ∨ T) is not a tautology?

tbhaxor

237 views

tbhaxor asked Mar 5

7 votes

2 answers

38

GO Classes CS 2025 | Weekly Quiz 3 | Propositional Logic | Question: 4
Consider the following arguments. $\text{Argument 1:}$ ... ? Only Argument $1$ is valid. Only Argument $2$ is valid. Both Arguments are valid. No Argument is valid.

Consider the following arguments.$\text{Argument 1:}$ Kerry errs or Myrna fails to show. If Kerry errs, then he does not break the record. Myrna fails to show. Therefore,...

GO Classes

464 views

GO Classes asked Apr 5, 2023

42 votes

4 answers

39

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

8.6k views

Kathleen asked Oct 8, 2014

4 votes

2 answers

40

GO Classes CS 2025 | Weekly Quiz 3 | Propositional Logic | Question: 6
The implies connective $\rightarrow$ is one of the stranger connectives in propositional logic. Below are a series of statements regarding implications. Which of the following statements is/are TRUE? For any propositions $P$ ... $R,$ the following statement is always true: $(P \rightarrow Q) \vee (R \rightarrow Q)$.

The “implies” connective “$\rightarrow$” is one of the stranger connectives in propositional logic. Below are a series of statements regarding implications.Which ...

GO Classes

358 views

GO Classes asked Apr 5, 2023

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