Recent questions tagged mathematical-logic / GATE Overflow for GATE CSE

2 votes

2 answers

331

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...

GO Classes

649 views

GO Classes asked Mar 23, 2022

4 votes

1 answer

332

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...

GO Classes

553 views

GO Classes asked Mar 23, 2022

9 votes

1 answer

333

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...

GO Classes

873 views

GO Classes asked Mar 23, 2022

4 votes

3 answers

334

GO Classes CS 2025 | Weekly Quiz 1 | Propositional Logic | Question: 3
Suppose that the statement $p \rightarrow \neg q$ is false. What is the number of all possible combinations of truth values of $r$ and $s$ for which $(\neg q \rightarrow r) \wedge (\neg p \vee s)$ is true?

Suppose that the statement $p \rightarrow \neg q$ is false. What is the number of all possible combinations of truth values of $r$ and $s$ for which $(\neg q \rightarrow ...

GO Classes

2.4k views

GO Classes asked Mar 23, 2022

5 votes

1 answer

335

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...

GO Classes

350 views

GO Classes asked Mar 23, 2022

11 votes

4 answers

336

GO Classes CS 2025 | Weekly Quiz 1 | Propositional Logic | Question: 13
The number of combinations of truth values for $p, q$ and $r$ for which the statement $\neg p \leftrightarrow (q \wedge \neg (p \rightarrow r))$ is true ________

The number of combinations of truth values for $p, q$ and $r$ for which the statement $\neg p \leftrightarrow (q \wedge \neg (p \rightarrow r))$ is true ________

GO Classes

1.2k views

GO Classes asked Mar 23, 2022

6 votes

1 answer

337

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...

GO Classes

962 views

GO Classes asked Mar 23, 2022

4 votes

2 answers

338

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...

GO Classes

552 views

GO Classes asked Mar 23, 2022

5 votes

1 answer

339

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 ...

GO Classes

540 views

GO Classes asked Mar 23, 2022

0 votes

0 answers

340

kenneth h rosen chapter 1 excercise 1.4 predicates and quantifiers question 46
Exercises 46-49 establish rules for null quantification that we can use when a quantified variable does not appear in part of a statement. 46. Establish these logical equivalences, where x does not occur as a free variable in A. Assume ... A ≡ ∃x(P (x) ∨ A) my doubt is wha is exactly A in in this logical expressions

Exercises 46–49 establish rules for null quantification thatwe can use when a quantified variable does not appear in partof a statement.46. Establish these logical equi...

ykrishnay

407 views

ykrishnay asked Mar 20, 2022

0 votes

1 answer

341

kenneth h rosen chapter 1 excercise 1.4 predicates ad quantifiers question 59 symbolic logic
Let P (x), Q(x), and R(x) be the statements x is a professor, x is ignorant, and x is vain, respectively. Express each of these statements using quantifiers; logical connectives; and P (x), Q(x), and ... c) follow from (a) and (b) what is the soution of d) cause i did not understand what the d) says?

Let P (x), Q(x), and R(x) be the statements“x is a professor,” “x is ignorant,” and “x is vain,” respectively.Express each of these statements using quantifie...

ykrishnay

1.2k views

ykrishnay asked Mar 19, 2022

0 votes

0 answers

342

kenneth h rosen chapter 1 excercise 1.4 predicates ad quantifiers question 33
Express each of these statements using quantifiers. Then form the negation of the statement, so that no negation is to the left of a quantifier. Next, express the negation in simple English. (Do not simply use the phrase It ... There is no dog that can talk. e) There is no one in this class who knows French and Russian.

Express each of these statements using quantifiers. Thenform the negation of the statement, so that no negationis to the left of a quantifier. Next, express the negation ...

ykrishnay

203 views

ykrishnay asked Mar 19, 2022

1 votes

1 answer

343

kenneth h rosen excercise 1.4 predicates and quantifiers question 22
22. For each of these statements find a domain for which the statement is true and a domain for which the statement is false. a) Everyone speaks Hindi. b) There is someone older than 21 years. c) Every two people have the same first name. d) Someone knows more than two other people.

22. For each of these statements find a domain for which thestatement is true and a domain for which the statement isfalse.a) Everyone speaks Hindi.b) There is someone ol...

ykrishnay

1.6k views

ykrishnay asked Mar 18, 2022

0 votes

2 answers

344

kenneth h rosen chapter 1 excercise 1.3
Show that (p → q) ∧ (q → r) and (p → r) is a logically equivalent to each other

Show that (p → q) ∧ (q → r) and (p → r) is a logically equivalent to each other

ykrishnay

602 views

ykrishnay asked Feb 22, 2022

0 votes

2 answers

345

kenneth h rosen chapter 1 excercise 1.3 question 47
Show that p NAND q is logically equivalent to ¬(p ∧ q). how to prove this and i prove using truth table which is easy but how to prove using logical identities ? thank you

Show that p NAND q is logically equivalent to ¬(p ∧ q).how to prove this and i prove using truth table which is easy but how to prove using logical identities ?thank y...

ykrishnay

550 views

ykrishnay asked Feb 21, 2022

0 votes

1 answer

346

Kenneth h rosen chapter 1 excercise 1.3 question 16
Each of Exercises 16-28 asks you to show that two compound propositions are logically equivalent. To do this, either show that both sides are true, or that both sides are false, for exactly the same combinations ... combinations of truth values of the propositional variables in these expressions i didnt understand what statement says please tell

Each of Exercises 16–28 asks you to show that two compoundpropositions are logically equivalent. To do this, either showthat both sides are true, or that both sides are...

ykrishnay

942 views

ykrishnay asked Feb 21, 2022

0 votes

2 answers

347

Kenneth h rosen chapter 1 excercise 1.2 question 15 on page 23
Each inhabitant of a remote village always tells the truth or always lies. A villager will give only a Yes or a No response to a question a tourist asks. Suppose you are a tourist visiting this area and come ... say 'yes'? how this question arise and please explain the reason about this answer to above question thank you

Each inhabitant of a remote village always tells the truth or always lies. A villager will give only a “Yes” or a “No” response to a question a tourist asks. Supp...

ykrishnay

725 views

ykrishnay asked Feb 16, 2022

0 votes

0 answers

348

Kenneth h roesn chapter-1 excercise 1.1 question 23's d) and e) question
in d. and e. i have a doubt can anyone resolve it ? doubt? d)It is necessary to walk 8 miles to get to the top of Long's Peak. if we compare with a necessary condition for p is q so i think it would ... famous. so it would be p→ q so (if get tenure as professor,then to be world famous) please resolve this confusion thank you

in d. and e. i have a doubt can anyone resolve it ?doubt?d)It is necessary to walk 8 miles to get to the top of Long’s Peak.if we compare with “a necessary condition ...

ykrishnay

266 views

ykrishnay asked Feb 13, 2022

2 votes

2 answers

349

TIFR CSE 2021 | Part B | Question: 1
Consider the following statements about propositional formulas. $\left ( p\wedge q \right )\rightarrow r$ and $\left ( p \rightarrow r \right )\wedge \left ( q\rightarrow r \right )$ are $\textit{not }$ ... values $p$ and $q$, $\text{(i)}$ can be either true or false, while $\text{(ii)}$ is always false.

Consider the following statements about propositional formulas.$\left ( p\wedge q \right )\rightarrow r$ and $\left ( p \rightarrow r \right )\wedge \left ( q\rightarrow ...

soujanyareddy13

896 views

soujanyareddy13 asked Mar 25, 2021

27 votes

9 answers

350

GATE CSE 2021 Set 2 | Question: 15
Choose the correct choice(s) regarding the following proportional logic assertion $S$: $S: (( P \wedge Q) \rightarrow R) \rightarrow (( P \wedge Q) \rightarrow (Q \rightarrow R))$ $S$ is neither a tautology nor a contradiction $S$ is a tautology $S$ is a contradiction The antecedent of $S$ is logically equivalent to the consequent of $S$

Choose the correct choice(s) regarding the following proportional logic assertion $S$:$$S: (( P \wedge Q) \rightarrow R) \rightarrow (( P \wedge Q) \rightarrow (Q \righta...

Arjun

9.0k views

Arjun asked Feb 18, 2021

14 votes

8 answers

351

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

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...

Arjun

8.4k views

Arjun asked Feb 18, 2021

6 votes

1 answer

352

NIELIT Scientist B 2020 November: 84
Given the truth table of a Binary Operation \$ as follows: $ ... hline \end{array}$ 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 }& ...

gatecse

677 views

gatecse asked Dec 9, 2020

tags	tag:apple
author	user:martin
title	title:apple
content	content:apple
exclude	-tag:apple
force match	+apple
views	views:100
score	score:10
answers	answers:2
is accepted	isaccepted:true
is closed	isclosed:true