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

4 votes

3 answers

511

TIFR CSE 2018 | Part B | Question: 4
The notation "$\Rightarrow$" denotes "implies" and "$\wedge$" denotes "and" in the following formulae. Let $X$ denote the formula: $(b \Rightarrow a ) \Rightarrow ( a \Rightarrow b)$ Let $Y$ denote the formula: ... is not satisfiable. $X$ is not tautology and $Y$ is satisfiable. $X$ is a tautology and $Y$ is satisfiable,

The notation "$\Rightarrow$" denotes "implies" and "$\wedge$" denotes "and" in the following formulae.Let $X$ denote the formula: $(b \Rightarrow a ) \Rightarrow ( a \Ri...

Arjun

1.9k views

Arjun asked Dec 10, 2017

3 votes

1 answer

512

PREDICATE LOGIC
Consider the following predicate statements. P1: ~$\forall$x ~(P(X)-->$\exists$yQ(y)) P2: $\exists$x(~P(x)$\vee$ $\exists$yQ(y)) P3: $\exists$x(~$\exists$yQ(y)-->~P(x)) P4: ~$\forall$x(P(X) $\wedge$ ~$\exists$Q(Y)) which of ... )P2,P3,P4 D)ALL OF THESE. P2 is trivial,but in others predicate i am not able to see how the scope of ~(negation) changes,with respect to parantheses..

Consider the following predicate statements.P1: ~$\forall$x ~(P(X) >$\exists$yQ(y))P2: $\exists$x(~P(x)$\vee$ $\exists$yQ(y))P3: $\exists$x(~$\exists$yQ(y) >~P(x))P4: ~$\...

junaid ahmad

865 views

junaid ahmad asked Nov 22, 2017

0 votes

0 answers

513

prepositional logic : For all is not perfect is equal to someone is not perfect or someone is perfect .

hem chandra joshi

281 views

hem chandra joshi asked Nov 21, 2017

–1 votes

1 answer

514

Gate Academy
Which of the following is valid first order formula?

Which of the following is valid first order formula?

Saikat Dutta

554 views

Saikat Dutta asked Nov 21, 2017

1 votes

2 answers

515

Tautology of contingency

Parshu gate

1.7k views

Parshu gate asked Nov 19, 2017

0 votes

1 answer

516

propositional Logic
What is the difference between => and <=> ?

What is the difference between = and <= ?

Parshu gate

480 views

Parshu gate asked Nov 18, 2017

1 votes

1 answer

517

Self Doubt on order of execution of statements in Propositional Logic for implication operator
What would be the execution order of the below statement? $A \implies B \implies C$

What would be the execution order of the below statement?$A \implies B \implies C$

Tuhin Dutta

1.2k views

Tuhin Dutta asked Nov 17, 2017

2 votes

2 answers

518

Discrete maths:- Predicate logic
Consider $F(P), Q(P), L(P)$ denotes statements Printer $P$ is out of service , Print job $P$ is queued and Print job $P$ ... $\forall j (Q(j) \wedge L(j)) \rightarrow \exists p F(P)$

Consider $F(P), Q(P), L(P)$ denotes statements “Printer $P$ is out of service”, “Print job $P$ is queued” and “Print job $P$ is lost” respectively. Then state...

rahul sharma 5

1.2k views

rahul sharma 5 asked Nov 16, 2017

0 votes

0 answers

519

Self doubt on First Order logic
To check whether this statement is always true $(\forall x (P(x)) \implies \forall x (Q(x))) \implies (\forall x(P(x) \implies Q(x)))$ Ans: Let $(\forall x (P(x)) \implies \forall x (Q(x)))$ ... A: T and B: F, hence the statement given in question cannot be valid or always true or tautology. Is my approach correct? Is this a correct solution?

To check whether this statement is always true$(\forall x (P(x)) \implies \forall x (Q(x))) \implies (\forall x(P(x) \implies Q(x)))$Ans:Let $(\forall x (P(x)) \implies \...

Tuhin Dutta

279 views

Tuhin Dutta asked Nov 16, 2017

2 votes

0 answers

520

propositional logic
If Salman Khan is guilty, then no witness is lying unless he is afraid. There is a witness who is afraid. Which of the following statements is true? (A) Salman Khan is guilty (B) Salman Khan is not guilty (C) There is a witness who is lying (D) From these facts one cannot conclude that Salman Khan is guilty

If Salman Khan is guilty, then no witness is lying unless he is afraid. There is a witness who is afraid. Which of the following statements is true? (A) Salman Khan i...

Parshu gate

314 views

Parshu gate asked Nov 14, 2017

1 votes

0 answers

521

discrete mathematics
plz explain this and suggest how to solve it rapidily?

plz explain this and suggest how to solve it rapidily?

Ravi prakash pandey

211 views

Ravi prakash pandey asked Nov 14, 2017

1 votes

1 answer

522

Discrete mathematics
is there any difference between in valid and tautology?

is there any difference between in valid and tautology?

Ravi prakash pandey

323 views

Ravi prakash pandey asked Nov 14, 2017

3 votes

1 answer

523

predicate logic
Recall that a predicate logic statement is contingent if its truth value depends on the choice of the universe and on the interpretations of the predicate symbol S and the constant symbol b involved. Consider the following predicate logic statements in which b, x ... - Contingent - Always false (C) Always true - Contingent - Contingent (D) Contingent - Always true - Always false

Recall that a predicate logic statement is contingent if its truth value depends on the choice of the universe and on the interpretations of the predicate symbol S and th...

Parshu gate

662 views

Parshu gate asked Nov 11, 2017

2 votes

1 answer

524

Ace Test Series: Mathematical Logic - Propositional Logic

hem chandra joshi

411 views

hem chandra joshi asked Nov 10, 2017

1 votes

1 answer

525

What do you mean by Necessarily true and not necessarily true in a statement?
Please explain it with an example, thank you!

Please explain it with an example, thank you!

iarnav

3.4k views

iarnav asked Oct 25, 2017

1 votes

1 answer

526

First Order Logic
A = ∃x (P(x) ^ Q(x)). B = ∃x P(x) ^ ∃x Q(x). Which is correct? a) A => B b) B => A c) A <=> B d) None of These Please Explain.

A = ∃x (P(x) ^ Q(x)).B = ∃x P(x) ^ ∃x Q(x).Which is correct?a) A = Bb) B = Ac) A <= Bd) None of ThesePlease Explain.

nishant279

1.3k views

nishant279 asked Oct 18, 2017

0 votes

0 answers

527

First Order Logic
A = ∃x(P(x)^Q(x)) B = ∃x P(x) ^ ∃x Q(x), which is correct? a) A <=> B b) A => B c) B => A d) None of These Please Explain.

A = ∃x(P(x)^Q(x))B = ∃x P(x) ^ ∃x Q(x), which is correct?a) A <= Bb) A = Bc) B = Ad) None of ThesePlease Explain.

nishant279

474 views

nishant279 asked Oct 18, 2017

0 votes

0 answers

528

Gate 2004| Logics| Let p,q,r, s be 4 primitive statements. Consider these arguments
I tried solving this question using normal approach of writing the whole truth table and evaluating each proposition. This seems to be a very error-prone method. It took over 15-20 minutes. Is there any other method of solving this kind of questions?

I tried solving this question using normal approach of writing the whole truth table and evaluating each proposition. This seems to be a very error-prone method. It took ...

rahul saxena

1.2k views

rahul saxena asked Oct 16, 2017

1 votes

1 answer

529

Kenneth Rosen Edition 6th Exercise 6.4 Question 39 (Page No. 442)
What is the generating function for the sequence of Fibonacci numbers?

What is the generating function for the sequence of Fibonacci numbers?

air1ankit

393 views

air1ankit asked Oct 9, 2017

3 votes

0 answers

530

#discrete mathematics
Are Conjunctive Normal Form and Disjunctive Normal Form included in the GATE syllabus?

Are Conjunctive Normal Form and Disjunctive Normal Form included in the GATE syllabus?

MrPeppermint

428 views

MrPeppermint asked Oct 8, 2017

1 votes

0 answers

531

Preposition Logic: Verify the solution
Which of the following propositional statements is TRUE ? A) ∀x ∀z ∃y [ P(x,y) ]---> ∃y ∀x ∀z [ P(x,y) ] B) ∃y ∀x ∀z [ P(x,y) ]---> ∀x ∀z ∃y [ P(x,y) ] I think in this A) False B) True Explanation:- Domain :- ... part is True. By the rule of implication, False -> True = True Finally conclude that: A) False B) True. Let me know where it is going wrong.

Which of the following propositional statements is TRUE ?A) ∀x ∀z ∃y [ P(x,y) ] - ∃y ∀x ∀z [ P(x,y) ]B) ∃y ∀x ∀z [ P(x,y) ] - ∀x ∀z ∃y [ P(x,y) ]I...

Shubhanshu

448 views

Shubhanshu asked Oct 6, 2017

0 votes

1 answer

532

discrete mathematics self doubt
how we come to know that whether in question we apply combination or permutation ..?? how can i make difference b/w both ?

how we come to know that whether in question we apply combination or permutation ..??how can i make difference b/w both ?

air1ankit

274 views

air1ankit asked Oct 3, 2017

0 votes

1 answer

533

UGC NET CSE | June 2009 | Part 2 | Question: 25
The prepositional formula given by the tree : is : ˄˅x2˅x1¬x1¬x1 (x2˅¬x2)˄(x1˅x2) (¬x1˅x2)˄(¬x1˅x2) None

The prepositional formula given by the tree :is :˄˅x2˅x1¬x1¬x1 (x2˅¬x2)˄(x1˅x2) (¬x1˅x2)˄(¬x1˅x2) None

rishu_darkshadow

588 views

rishu_darkshadow asked Sep 22, 2017

0 votes

0 answers

534

Propositional and First Order Logic GATE-CS-2006
In the question whether this statement is a tautology ((A ∨ B) → C)) ≡ ((A → C) ∨ (B → C)) , If I take first part ((A ∨ B) → C)) as P and second part ((A → C) ∨ (B → C)) as Q , do I need to prove P-->Q is true? or both P-->Q and Q-->P as true? I am confused about the ≡ symbol.

In the question whether this statement is a tautology ((A ∨ B) → C)) ≡ ((A → C) ∨ (B → C)) ,If I take first part ((A ∨ B) → C)) as P and second part ((A...

preps

1.1k views

preps asked Sep 17, 2017

4 votes

1 answer

535

Kenneth Rosen Edition 6th Exercise 1.3 Question 48 (Page No. 50)
Establish these logical equivalences, where x does not occur as a free variable in A. Assume that the domain is nonempty. a) ∀x(A → P(x)) ≡ A → ∀xP(x) b) ∃x(A → P(x)) ≡ A → ∃xP(x)

Establish these logical equivalences, where x does not occur as a free variable in A. Assume that the domain is nonempty.a) ∀x(A → P(x)) ≡ A → ∀xP(x)b) ∃x(A �...

Manu Thakur

3.3k views

Manu Thakur asked Sep 13, 2017

4 votes

1 answer

536

Propositional Logic
Can someone please check if my solution is correct?

Can someone please check if my solution is correct?

Manu Thakur

668 views

Manu Thakur asked Sep 13, 2017

0 votes

0 answers

537

MadeEasy Workbook: Mathematical Logic - Propositional Logic
Show that each of the conditional statement is a tautology NOT using a truth table $r\vee (p\vee q)$ is the conclusion from the premises $(p \vee q) \wedge(q\rightarrow r)\wedge (p\rightarrow m) \wedge (m')$

Show that each of the conditional statement is a tautology NOT using a truth table$r\vee (p\vee q)$ is the conclusion from the premises $(p \vee q) \wedge(q\rightarrow r)...

Agnel A

326 views

Agnel A asked Sep 3, 2017

1 votes

0 answers

538

GATE-1997 (1-marks question) logic function and minimization
Let * be define as x*y=x'+y. let z=x*y value of z*x is ... 1>x'+y 2>x 3>0 4>1

Let * be define as x*y=x'+y. let z=x*y value of z*x is ...1>x'+y2>x3>04>1

air1ankit

513 views

air1ankit asked Sep 1, 2017

1 votes

1 answer

539

Discrete Mathematics practice ques
provide negation of each of the statements

provide negation of each of the statements

Pavan Kumar Munnam

487 views

Pavan Kumar Munnam asked Aug 31, 2017

3 votes

1 answer

540

Quantifier
Express the statement If a person is female and is a parent, then this person is someone's mother as a logical expression involving predicates, quantifiers with a domain consisting of all people, and logical connectives. F(x) to represent x is female, P(x) to represent x is a parent, and M(x, y) to ... ?pls explain ∀x((F (x) ∧ P(x)) → ∃yM(x, y)). ∀x∃y((F (x) ∧ P(x)) → M(x, y)).

Express the statement “If a person is female and is a parent, then this person is someone’smother” as a logical expression involving predicates, quantifiers with a ...

set2018

2.4k views

set2018 asked Aug 27, 2017

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