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Recent questions tagged propositional-logic
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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
Mathematical Logic
discrete-mathematics
propositional-logic
mathematical-logic
engineering-mathematics
kenneth-rosen
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0
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1
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212
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
Mathematical Logic
discrete-mathematics
propositional-logic
mathematical-logic
engineering-mathematics
kenneth-rosen
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0
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213
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
Mathematical Logic
discrete-mathematics
propositional-logic
mathematical-logic
engineering-mathematics
kenneth-rosen
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1
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1
answer
214
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
Mathematical Logic
discrete-mathematics
propositional-logic
mathematical-logic
engineering-mathematics
kenneth-rosen
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0
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2
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215
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
599
views
ykrishnay
asked
Feb 22, 2022
Mathematical Logic
discrete-mathematics
mathematical-logic
propositional-logic
engineering-mathematics
kenneth-rosen
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1
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2
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216
Kenneth Rosen Edition 7 Excercise 1.3 Question 56 (Page No. 36)
Show that if p, q, and r are compound propositions such that p and q are logically equivalent and q and r are logically equivalent, then p and r are logically equivalent.
Show that if p, q, and r are compound propositions such that p and q are logically equivalent and q and r are logically equivalent, then p and r are logically equivalent....
ykrishnay
1.4k
views
ykrishnay
asked
Feb 21, 2022
Mathematical Logic
kenneth-rosen
discrete-mathematics
propositional-logic
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0
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2
answers
217
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
549
views
ykrishnay
asked
Feb 21, 2022
Mathematical Logic
discrete-mathematics
mathematical-logic
propositional-logic
engineering-mathematics
kenneth-rosen
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0
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1
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218
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
Mathematical Logic
discrete-mathematics
mathematical-logic
propositional-logic
engineering-mathematics
kenneth-rosen
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2
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219
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
724
views
ykrishnay
asked
Feb 16, 2022
Mathematical Logic
discrete-mathematics
mathematical-logic
propositional-logic
engineering-mathematics
kenneth-rosen
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220
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
Mathematical Logic
mathematical-logic
propositional-logic
discrete-mathematics
engineering-mathematics
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221
Propositional Logic | Made Easy Full Syllabus Test
How is B a tautology?
How is B a tautology?
palashbehra5
527
views
palashbehra5
asked
Jan 14, 2022
Mathematical Logic
made-easy-test-series
propositional-logic
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2
votes
2
answers
222
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
894
views
soujanyareddy13
asked
Mar 25, 2021
Mathematical Logic
tifr2021
mathematical-logic
propositional-logic
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27
votes
9
answers
223
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 $S$:$$S: (( P \wedge Q) \rightarrow R) \rightarrow (( P \wedge Q) \rightarrow (Q \righta...
Arjun
9.0k
views
Arjun
asked
Feb 18, 2021
Mathematical Logic
gatecse-2021-set2
multiple-selects
mathematical-logic
propositional-logic
1-mark
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14
votes
8
answers
224
GATE CSE 2021 Set 1 | Question: 7
Let $p$ and $q$ be two propositions. Consider the following two formulae in propositional logic. $S_1: (\neg p\wedge(p\vee q))\rightarrow q$ $S_2: q\rightarrow(\neg p\wedge(p\vee q))$ Which one of the following choices is correct? Both $S_1$ and ... but $S_2$ is not a tautology $S_1$ is not a tautology but $S_2$ is a tautology Neither $S_1$ nor $S_2$ is a tautology
Let $p$ and $q$ be two propositions. Consider the following two formulae in propositional logic.$S_1: (\neg p\wedge(p\vee q))\rightarrow q$$S_2: q\rightarrow(\neg p\wedge...
Arjun
8.4k
views
Arjun
asked
Feb 18, 2021
Mathematical Logic
gatecse-2021-set1
mathematical-logic
propositional-logic
1-mark
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6
votes
1
answer
225
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:$$\begin{array}{|l|l|l|l|} \hline {} \text{X} & \text{Y }& \text{X\$Y }\\ \hline \text{1} & \text{0 }& ...
gatecse
673
views
gatecse
asked
Dec 9, 2020
Mathematical Logic
nielit-scb-2020
mathematical-logic
propositional-logic
discrete-mathematics
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2
votes
1
answer
226
UGC NET CSE | October 2020 | Part 2 | Question: 61
Consider the statement below. A person who is radical $(R)$ is electable $(E)$ if he/she is conservative $(C)$, but otherwise not electable. Few probable logical assertions of the above sentence are given below. $(R \wedge E) \Leftrightarrow C$ ... given below: $(ii)$ only $(iii)$ only $(i)$ and $(iii)$ only $(ii)$ and $(iv)$ only
Consider the statement below.A person who is radical $(R)$ is electable $(E)$ if he/she is conservative $(C)$, but otherwise not electable.Few probable logical assertions...
go_editor
2.1k
views
go_editor
asked
Nov 20, 2020
Mathematical Logic
ugcnetcse-oct2020-paper2
discrete-mathematics
propositional-logic
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2
votes
3
answers
227
NIELIT 2017 July Scientist B (IT) - Section B: 13
Which of the following statements is false? $(P\land Q)\lor(\sim P\land Q)\lor(P \land \sim Q)$ is equal to $\sim Q\land \sim P$ $(P\land Q)\lor(\sim P\land Q)\lor(P \wedge \sim Q)$ is equal to $Q\lor P$ ... $(P\land Q)\lor(\sim P\land Q)\lor (P \land \sim Q)$ is equal to $P\lor (Q\land \sim P)$
Which of the following statements is false?$(P\land Q)\lor(\sim P\land Q)\lor(P \land \sim Q)$ is equal to $\sim Q\land \sim P$$(P\land Q)\lor(\sim P\land Q)\lor(P \wedge...
admin
888
views
admin
asked
Mar 30, 2020
Mathematical Logic
nielit2017july-scientistb-it
mathematical-logic
propositional-logic
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0
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1
answer
228
UGC NET CSE | December 2006 | Part 2 | Question: 2
The proposition ~ q ∨ p is equivalent to :
The proposition ~ q ∨ p is equivalent to :
go_editor
595
views
go_editor
asked
Mar 27, 2020
Mathematical Logic
ugcnetcse-dec2006-paper2
mathematical-logic
propositional-logic
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–
1
votes
1
answer
229
UGC NET CSE | January 2017 | Part 3 | Question: 59
Which of the following statements is true? The sentence $S$ is a logical consequence of $S_{1},\dots,S_{n}$ if and only if $S_{1}\wedge S_{2} \wedge \dots \wedge S_{n}\rightarrow S$ is satisfiable. The sentence $S$ ... $S_{1}\wedge S_{2}\wedge \dots \wedge S_{n}\wedge S$ is inconsistent.
Which of the following statements is true?The sentence $S$ is a logical consequence of $S_{1},\dots,S_{n}$ if and only if $S_{1}\wedge S_{2} \wedge \dots \wedge S_{n}\ri...
go_editor
3.7k
views
go_editor
asked
Mar 24, 2020
Mathematical Logic
ugcnetcse-jan2017-paper3
mathematical-logic
propositional-logic
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3
votes
6
answers
230
UGC NET CSE | January 2017 | Part 2 | Question: 6
In propositional logic if $\left ( P \rightarrow Q \right )\wedge \left ( R \rightarrow S \right )$ and $\left ( P \vee R \right )$ are two premises such that $\begin{array}{c} (P \to Q) \wedge (R \to S) \\ P \vee R \\ \hline Y \\ \hline \end{array}$ $Y$ is the premise : $P \vee R$ $P \vee S$ $Q \vee R$ $Q \vee S$
In propositional logic if $\left ( P \rightarrow Q \right )\wedge \left ( R \rightarrow S \right )$ and $\left ( P \vee R \right )$ are two premises such that$$\begin{arr...
go_editor
3.0k
views
go_editor
asked
Mar 24, 2020
Mathematical Logic
ugcnetjan2017ii
discrete-mathematics
propositional-logic
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6
votes
2
answers
231
UGC NET CSE | June 2019 | Part 2 | Question: 6
Which of the following is principal conjunctive normal form for $[(p\vee q)\wedge\ \neg p \rightarrow \neg q ]$ ? $p\ \vee \neg q$ $p \vee q $ $\neg p \vee q$ $\neg p\ \vee \neg q$
Which of the following is principal conjunctive normal form for $[(p\vee q)\wedge\ \neg p \rightarrow \neg q ]$ ?$p\ \vee \neg q$$p \vee q $$\neg p \vee q$$\neg p\ \vee ...
Arjun
7.7k
views
Arjun
asked
Jul 2, 2019
Mathematical Logic
ugcnetcse-june2019-paper2
propositional-logic
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6
votes
3
answers
232
UGC NET CSE | June 2019 | Part 2 | Question: 8
Match List-I with List-II: ... ); (b) - (i); (c) - (iii); (d) - (ii) (a) - (iv); (b) - (iii); (c) - (i); (d) - (ii)
Match List-I with List-II:$$\begin{array}{|c|c|c|c|} \hline {} & \text{List-I} & {} & \text{List-II} \\ \hline (a) & p \rightarrow q & (i) & \rceil ( q \rightarrow \rcei...
Arjun
1.9k
views
Arjun
asked
Jul 2, 2019
Mathematical Logic
ugcnetcse-june2019-paper2
propositional-logic
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3
votes
1
answer
233
Proposition Logic Question
Are these propositions? 1.This sentence is true 2.This sentence is false Aren’t these liar paradox?
Are these propositions?1.This sentence is true2.This sentence is falseAren’t these liar paradox?
Reshu $ingh
1.9k
views
Reshu $ingh
asked
May 30, 2019
Mathematical Logic
mathematical-logic
propositional-logic
discrete-mathematics
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