Recent questions tagged goclasses_wq3 / GATE Overflow for GATE CSE

4 votes

1 answer

1

GO Classes 2023 | Weekly Quiz 3 | Question: 1
If $F_1, F_2$ and $F_3$ are propositional formulae/expressions, over same set of propositional variables, such that $F_1\wedge F_2\rightarrow F_3$ is a contradiction, then which of the following is/are necessarily true? Both $F_1$ and $F_2$ ... $F_1\wedge F_2$ is a tautology $F_3$ is a contradiction $F_1,\;F_2$ and $F_3$ all are contradictions.

If $F_1, F_2$ and $F_3$ are propositional formulae/expressions, over same set of propositional variables, such that $F_1\wedge F_2\rightarrow F_3$ is a contradiction, the...

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GO Classes asked Mar 23, 2022

4 votes

1 answer

2

GO Classes 2023 | Weekly Quiz 3 | Question: 2
If $F_1, F_2$ and $F_3$ are propositional formulae/expressions, over same set of propositional variables, such that $(F_1\rightarrow F_2)\rightarrow F_3$ is a contradiction, then which of the following is/are necessarily true? It is not ... Contradiction. $F_3$ is a contradiction. It is not possible that $F_1$ is Contingency and $F_2$ is Contradiction.

If $F_1, F_2$ and $F_3$ are propositional formulae/expressions, over same set of propositional variables, such that $(F_1\rightarrow F_2)\rightarrow F_3$ is a contradicti...

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GO Classes asked Mar 23, 2022

3 votes

2 answers

3

GO Classes 2023 | Weekly Quiz 3 | Question: 3
Here are some very useful ways of characterizing propositional formulas. Start by constructing a truth table for the formula and look at the column of values obtained. We say that the formula is: satisfiable if there is at least one $T$ ... Necessarily false: $F2$ is tautology $F3$ is tautology $F1$ is a contingency. $F1\wedge F3$ is contradiction.

Here are some very useful ways of characterizing propositional formulas. Start by constructing a truth table for the formula and look at the column of values obtained. We...

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GO Classes asked Mar 23, 2022

5 votes

2 answers

4

GO Classes 2023 | Weekly Quiz 3 | Question: 4
Let $A,\;B$ represent two propositions. Which of the following logical formulae is/are tautology? $A\wedge B\rightarrow (A\rightarrow B)$ $A\wedge \neg B \rightarrow \neg (A\rightarrow B)$ $\neg A\wedge B \rightarrow (A\rightarrow B)$ $\neg A\wedge \neg B \rightarrow (A\rightarrow B)$

Let $A,\;B$ represent two propositions.Which of the following logical formulae is/are tautology?$A\wedge B\rightarrow (A\rightarrow B)$$A\wedge \neg B \rightarrow \neg (A...

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527 views

GO Classes asked Mar 23, 2022

4 votes

1 answer

5

GO Classes 2023 | Weekly Quiz 3 | Question: 5
Let’s consider the interpretation $v$ where $v(p) = F, v(q) = T, v(r) = T.$ Which of the following propositional formulas are satisfied by $v$? $(p \rightarrow \neg q) \vee \neg(r \wedge q)$ $(\neg p \vee \neg q) \rightarrow (p \vee \neg r)$ $\neg(\neg p \rightarrow \neg q) \wedge r$ $\neg (\neg p \rightarrow q \wedge \neg r)$

Let’s consider the interpretation $v$ where $v(p) = F, v(q) = T, v(r) = T.$ Which of the following propositional formulas are satisfied by $v$?$(p \rightarrow \neg q) \...

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841 views

GO Classes asked Mar 23, 2022

5 votes

1 answer

6

GO Classes 2023 | Weekly Quiz 3 | Question: 6
If $F1$, and $F2$ are propositional formulae/expressions, over same set of propositional variables, such that $F1,F2$ both are contingencies, then which of the following is/are necessarily false(i.e. Never Possible): $F1 \vee F2$ is a ... a tautology. $F1 \vee F2$ is a contradiction $(F1 \rightarrow F2) \vee (F2 \rightarrow F1)$ is contingency.

If $F1$, and $F2$ are propositional formulae/expressions, over same set of propositional variables, such that $F1,F2$ both are contingencies, then which of the following ...

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GO Classes asked Mar 23, 2022

4 votes

1 answer

7

GO Classes 2023 | Weekly Quiz 3 | Question: 7
Let $p,q$ be two atomic propositional assertions. Then which of the following is/are false? $(p \rightarrow q) \vee (p \rightarrow \neg q)$ is a tautology. $(p \rightarrow q) \vee (q \rightarrow p)$ is a tautology. $(p \rightarrow q) \vee (q \rightarrow \neg p)$ is a tautology. $(p \rightarrow q) \vee (\neg q \rightarrow \neg p)$ is a tautology.

Let $p,q$ be two atomic propositional assertions. Then which of the following is/are false?$(p \rightarrow q) \vee (p \rightarrow \neg q)$ is a tautology.$(p \rightarrow ...

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419 views

GO Classes asked Mar 23, 2022

3 votes

2 answers

8

GO Classes 2023 | Weekly Quiz 3 | Question: 9
Consider the statement form $S$ : $\left((p\Rightarrow (q\Rightarrow r)) \Leftrightarrow ((p\wedge q)\Rightarrow r)\right)\wedge \sim p\wedge \sim q\wedge \sim r$ Which of the following is true ? $S$ is a tautology $S$ is a Contradiction $S$ is a Contingency $S$ is equivalent to $ \sim (p\vee q\vee r)$.

Consider the statement form $S$ :$\left((p\Rightarrow (q\Rightarrow r)) \Leftrightarrow ((p\wedge q)\Rightarrow r)\right)\wedge \sim p\wedge \sim q\wedge \sim r$Which of ...

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667 views

GO Classes asked Mar 23, 2022

4 votes

3 answers

9

GO Classes 2023 | Weekly Quiz 3 | Question: 10
The shortest formula in propositional logic is $’p’$ where $p$ is a propositional atom. Which one of the following statements is TRUE? The formula $p$ is valid and satisfiable. The formula $p$ is invalid and unsatisfiable. The formula $p$ is invalid and satisfiable. The formula $p$ is valid and unsatisfiable.

The shortest formula in propositional logic is $’p’$ where $p$ is a propositional atom.Which one of the following statements is TRUE?The formula $p$ is valid and sati...

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704 views

GO Classes asked Mar 23, 2022

5 votes

2 answers

10

GO Classes 2023 | Weekly Quiz 3 | Question: 12
An island has two kinds of inhabitants, knights, who always tell the truth, and knaves, who always lie. You encounter two people $A$ and $B$. What are $A$ and $B$ if: $A$ says $B$ is a knight and $B$ says The two of us are opposite types ? $A$ is ... , $B$ is knight $B$ is knight, $B$ is knave. $A$ is knave, $B$ is knave. $A$ is knave, $B$ is knight

An island has two kinds of inhabitants, knights, who always tell the truth, and knaves, who always lie. You encounter two people $A$ and $B$. What are $A$ and $B$ if: $A$...

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590 views

GO Classes asked Mar 23, 2022

2 votes

2 answers

11

GO Classes 2023 | Weekly Quiz 3 | Question: 13
Consider the following proposition : $A_n=\underbrace{(p\rightarrow (q\rightarrow (p\rightarrow (q\rightarrow (\dots )))))}_{\text{number of p's+ number of q's = n}}$ Which of the following is true for $A_n$ : For every $n \geq 2$, ... $n \geq 2$, $A_n$ is a contingency. For every $n \geq 2$, $A_n$ is either a tautology or a contingency.

Consider the following proposition :$A_n=\underbrace{(p\rightarrow (q\rightarrow (p\rightarrow (q\rightarrow (\dots )))))}_{\text{number of p's+ number of q's = n}}$Which...

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646 views

GO Classes asked Mar 23, 2022

4 votes

1 answer

12

GO Classes 2023 | Weekly Quiz 3 | Question: 14
If $F1, F2$ and $F3$ are propositional formulae/expressions, over same set of propositional variables, such that $F1 \wedge F2 \wedge F3$ is unsatisfiable and such that the conjunction of any pair of them is satisfiable, then which of the ... $(F1\rightarrow F2),(F2\rightarrow F3),(F3\rightarrow F1)$, all are contingency.

If $F1, F2$ and $F3$ are propositional formulae/expressions, over same set of propositional variables, such that $F1 \wedge F2 \wedge F3$ is unsatisfiable and such that t...

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551 views

GO Classes asked Mar 23, 2022

9 votes

1 answer

13

GO Classes 2023 | Weekly Quiz 3 | Question: 15
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, then $G$ ... $(F \rightarrow G) \wedge (F \rightarrow \neg G)$ 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...

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870 views

GO Classes asked Mar 23, 2022

5 votes

1 answer

14

GO Classes 2023 | Weekly Quiz 3 | Question: 17
If the statement $q \wedge r$ is true, then the number of all combinations of truth values for $p$ and $s$ such that the statement $(q \rightarrow [\neg p \vee s]) \wedge [\neg s \rightarrow r]$ is TRUE is ______

If the statement $q \wedge r$ is true, then the number of all combinations of truth values for $p$ and $s$ such that the statement $(q \rightarrow [\neg p \vee s]) \wedge...

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350 views

GO Classes asked Mar 23, 2022

6 votes

1 answer

15

GO Classes 2023 | Weekly Quiz 3 | Question: 19
Let $F$ and $G$ be two propositional formula. Which of the following is/are TRUE? If $F \rightarrow G$ is satisfiable and $F$ is satisfiable, then $G$ is satisfiable. If two statements(propositions) are logically equivalent, then so are their ... . If a statement $q$ is true, then, for any statement $p$, the statement $p \rightarrow q$ is true.

Let $F$ and $G$ be two propositional formula. Which of the following is/are TRUE?If $F \rightarrow G$ is satisfiable and $F$ is satisfiable, then $G$ is satisfiable.If tw...

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957 views

GO Classes asked Mar 23, 2022

4 votes

2 answers

16

GO Classes 2023 | Weekly Quiz 3 | Question: 20
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 $P$ and $Q,$ the following is ... $R,$ 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...

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548 views

GO Classes asked Mar 23, 2022

5 votes

1 answer

17

GO Classes 2023 | Weekly Quiz 3 | Question: 21
Of all the connectives we've seen, the implication $\rightarrow$ connective is probably the trickiest. Let $F$ and $G$ be two propositional formulas, over same set of propositional variables, such that $(F \rightarrow G)$ ... $(F \rightarrow G)\wedge (G \rightarrow F)$ is necessarily a Tautology. $F$ is necessarily equivalent to $G.$

Of all the connectives we've seen, the implication “$\rightarrow$” connective is probably the trickiest. Let $F$ and $G$ be two propositional formulas, over same set ...

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GO Classes asked Mar 23, 2022

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