Recent questions tagged mathematical-logic

Recent questions tagged mathematical-logic

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GATE CSE Question
Consider the following statements about a group G ? (I) G must be abelian if $(ab)^{2}$ = $a^2$b^2$, $\forall a,b\epsilon G$ (II) G is abelian if x = $x^{-1}$, $\forall x$\epsilon$G Options are: I is true II is true Both I and II are true None

rsansiya111 asked in Mathematical Logic Nov 29, 2021

9 views

1 vote

1 answer

2

TIFR2021-B: 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 $\textit{not }$ ... on the values $p$ and $q$, $\text{(i)}$ can be either true or false, while $\text{(ii)}$ is always false.

soujanyareddy13 asked in Others Mar 25, 2021

by soujanyareddy13

311 views

8 votes

4 answers

3

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 $S$

Arjun asked in Mathematical Logic Feb 18, 2021

by Arjun

2.4k views

4 votes

4 answers

4

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

Arjun asked in Mathematical Logic Feb 18, 2021

by Arjun

2.4k views

1 vote

2 answers

5

UGCNET-Oct2020-II: 3
Which of the following pairs of propositions are not logically equivalent? $((p \rightarrow r) \wedge (q \rightarrow r))$ and $((p \vee q) \rightarrow r)$ $p \leftrightarrow q$ and $(\neg p \leftrightarrow \neg q)$ $((p \wedge q) \vee (\neg p \wedge \neg q))$ and $p \leftrightarrow q$ $((p \wedge q) \rightarrow r)$ and $((p \rightarrow r) \wedge (q \rightarrow r))$

jothee asked in Discrete Mathematics Nov 20, 2020

by jothee

1.2k views

0 votes

1 answer

6

UGCNET-Oct2020-II: 37
If $f(x)=x$ is my friend, and $p(x) =x$ is perfect, then correct logical translation of the statement “some of my friends are not perfect” is ______ $\forall _x (f(x) \wedge \neg p(x))$ $\exists _x (f(x) \wedge \neg p(x))$ $\neg (f(x) \wedge \neg p(x))$ $\exists _x (\neg f(x) \wedge \neg p(x))$

jothee asked in Discrete Mathematics Nov 20, 2020

by jothee

451 views

0 votes

1 answer

7

UGCNET-Oct2020-II: 38
What kind of clauses are available in conjunctive normal form? Disjunction of literals Disjunction of variables Conjunction of literals Conjunction of variables

jothee asked in Discrete Mathematics Nov 20, 2020

by jothee

557 views

1 vote

2 answers

8

NIELIT 2016 MAR Scientist C - Section C: 25
Which of the following is FALSE? $Read\ \wedge as\ AND, \vee\ as\ OR, \sim as\ NOT, \rightarrow$ as one way implication and $\leftrightarrow$ as two way implication? $((x\rightarrow y)\wedge x)\rightarrow y$ $((\sim x\rightarrow y)\wedge (\sim x\wedge \sim y))\rightarrow x$ $(x\rightarrow (x\vee y))$ $((x\vee y)\leftrightarrow (\sim x\vee \sim y))$

Lakshman Patel RJIT asked in Mathematical Logic Apr 2, 2020

by Lakshman Patel RJIT

268 views

0 votes

4 answers

9

NIELIT 2016 MAR Scientist C - Section C: 65
In propositional logic, which of the following is equivalent to $p \rightarrow q$? $\sim p\rightarrow q$ $ \sim p \vee q$ $ \sim p \vee \sim q$ $p\rightarrow \sim q$

Lakshman Patel RJIT asked in Mathematical Logic Apr 2, 2020

by Lakshman Patel RJIT

926 views

2 votes

3 answers

10

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 $P\lor (Q\land \sim P)$

Lakshman Patel RJIT asked in Mathematical Logic Mar 30, 2020

by Lakshman Patel RJIT

421 views

1 vote

3 answers

11

NIELIT 2017 July Scientist B (CS) - Section B: 16
Which of the following propositions is tautology? $(p\lor q)\to q$ $p\lor (q\to p)$ $p\lor (p\to q)$ Both (B) and (C)

Lakshman Patel RJIT asked in Mathematical Logic Mar 30, 2020

by Lakshman Patel RJIT

389 views

0 votes

3 answers

12

NIELIT 2017 DEC Scientist B - Section B: 43
Which one is the correct translation of the following statement into mathematical logic? “None of my friends are perfect.” $\neg\:\exists\:x(p(x)\land q(x))$ $\exists\:x(\neg\:p(x)\land q(x))$ $\exists\:x(\neg\:p(x)\land\neg\:q(x))$ $\exists\:x(p(x)\land\neg\:q(x))$

Lakshman Patel RJIT asked in Mathematical Logic Mar 30, 2020

by Lakshman Patel RJIT

636 views

0 votes

1 answer

13

UGCNET-Dec2006-II: 2
The proposition ~ q ∨ p is equivalent to :

jothee asked in Mathematical Logic Mar 27, 2020

by jothee

286 views

0 votes

1 answer

14

UGCNET-Jan2017-III: 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 $S$ ... of $S_{1},\dots,S_{n}$ if and only if $S_{1}\wedge S_{2}\wedge \dots \wedge S_{n}\wedge S$ is inconsistent.

jothee asked in Discrete Mathematics Mar 24, 2020

by jothee

968 views

0 votes

3 answers

15

UGCNET-Jan2017-II: 2
Match the following : ...

jothee asked in Mathematical Logic Mar 24, 2020

by jothee

330 views

20 votes

6 answers

16

GATE CSE 2020 | Question: 39
Which one of the following predicate formulae is NOT logically valid? Note that $W$ is a predicate formula without any free occurrence of $x$. $\forall x (p(x) \vee W) \equiv \forall x \: ( px) \vee W$ ... $\exists x(p(x) \rightarrow W) \equiv \forall x \: p(x) \rightarrow W$

Arjun asked in Mathematical Logic Feb 12, 2020

by Arjun

7.7k views

6 votes

3 answers

17

ISRO2020-73
Given that $B(a)$ means “$a$ is a bear” $F(a)$ means “$a$ is a fish” and $E(a,b)$ means “$a $ eats $b$” Then what is the best meaning of $\forall x [F(x) \to \forall y(E(y,x)\rightarrow b(y))]$ Every fish is eaten by some bear Bears eat only fish Every bear eats fish Only bears eat fish

Satbir asked in Mathematical Logic Jan 13, 2020

by Satbir

1.5k views

2 votes

2 answers

18

CMI2019-B-5
In the land of Twitter, there are two kinds of people: knights (also called outragers), who always tell the truth, and knaves (also called trolls), who always lie. It so happened that a person with handle @anand tweeted something offensive. It was not known ... $3:$ My lawyer always tells the truth. Which of the above suspects are innocent, and which are guilty? Explain your reasoning.

gatecse asked in Mathematical Logic Sep 13, 2019

350 views

3 votes

1 answer

19

Mathematical Logic Ques:Self doubt
“Not every satisfiable logic is valid” Representation of it will be $1)\sim \left ( \forall S(x)\rightarrow V(x) \right )$ or $2)\sim \left ( \forall S(x)\vee V(x) \right )$ Among $1)$ and $2)$, which one is correct? and why?

srestha asked in Mathematical Logic Jun 4, 2019

545 views

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