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Recent questions tagged propositional-logic
41
votes
9
answers
661
GATE IT 2004 | Question: 31
Let $p, q, r$ and $s$ be four primitive statements. Consider the following arguments: $P: [(¬p\vee q) ∧ (r → s) ∧ (p \vee r)] → (¬s → q)$ $Q: [(¬p ∧q) ∧ [q → (p → r)]] → ¬r$ $R: [[(q ∧ r) → p] ∧ (¬q \vee p)] → r$ $S: [p ∧ (p → r) ∧ (q \vee ¬ r)] → q$ Which of the above arguments are valid? $P$ and $Q$ only $P$ and $R$ only $P$ and $S$ only $P, Q, R$ and $S$
Ishrat Jahan
asked
in
Mathematical Logic
Nov 2, 2014
by
Ishrat Jahan
11.7k
views
gateit-2004
mathematical-logic
normal
propositional-logic
29
votes
10
answers
662
GATE CSE 1996 | Question: 2.3
Which of the following is NOT True? (Read $\wedge$ as AND, $\vee$ as OR, $\neg$ as NOT, $\rightarrow$ as one way implication and $\leftrightarrow$ as two way implication) $((x \rightarrow y) \wedge x) \rightarrow y$ ... $(x \rightarrow (x \vee y))$ $((x \vee y) \leftrightarrow (\neg x \rightarrow \neg y))$
Kathleen
asked
in
Mathematical Logic
Oct 9, 2014
by
Kathleen
8.3k
views
gate1996
mathematical-logic
normal
propositional-logic
21
votes
3
answers
663
GATE CSE 1995 | Question: 13
Obtain the principal (canonical) conjunctive normal form of the propositional formula $(p \wedge q) \vee (\neg q \wedge r)$ where $\wedge$ is logical and, $\vee$ is inclusive or and $\neg$ is negation.
Kathleen
asked
in
Mathematical Logic
Oct 8, 2014
by
Kathleen
4.2k
views
gate1995
mathematical-logic
propositional-logic
normal
descriptive
41
votes
4
answers
664
GATE CSE 1995 | Question: 2.19
If the proposition $\lnot p \to q$ is true, then the truth value of the proposition $\lnot p \lor \left ( p \to q \right )$, where $\lnot$ is negation, $\lor$ is inclusive OR and $\to$ is implication, is True Multiple Values False Cannot be determined
Kathleen
asked
in
Mathematical Logic
Oct 8, 2014
by
Kathleen
8.5k
views
gate1995
mathematical-logic
normal
propositional-logic
22
votes
3
answers
665
GATE CSE 1994 | Question: 3.13
Let $p$ and $q$ be propositions. Using only the Truth Table, decide whether $p \Longleftrightarrow q$ does not imply $p \to \lnot q$ is True or False.
Kathleen
asked
in
Mathematical Logic
Oct 5, 2014
by
Kathleen
7.3k
views
gate1994
mathematical-logic
normal
propositional-logic
true-false
18
votes
3
answers
666
GATE CSE 1993 | Question: 18
Show that proposition $C$ is a logical consequence of the formula$A\wedge \left(A \to \left(B \vee C\right)\right) \wedge \left( B \to \neg A\right)$using truth tables.
Kathleen
asked
in
Mathematical Logic
Sep 29, 2014
by
Kathleen
3.1k
views
gate1993
mathematical-logic
normal
propositional-logic
proof
descriptive
23
votes
4
answers
667
GATE CSE 1993 | Question: 8.2
The proposition $p \wedge (\sim p \vee q)$ is: a tautology logically equivalent to $p \wedge q$ logically equivalent to $p \vee q$ a contradiction none of the above
Kathleen
asked
in
Mathematical Logic
Sep 29, 2014
by
Kathleen
8.2k
views
gate1993
mathematical-logic
easy
propositional-logic
17
votes
3
answers
668
GATE CSE 1997 | Question: 3.2
Which of the following propositions is a tautology? $(p \vee q) \rightarrow p$ $p \vee (q \rightarrow p)$ $p \vee (p \rightarrow q)$ $p \rightarrow (p \rightarrow q)$
Kathleen
asked
in
Mathematical Logic
Sep 29, 2014
by
Kathleen
6.1k
views
gate1997
mathematical-logic
easy
propositional-logic
53
votes
5
answers
669
GATE CSE 2014 Set 3 | Question: 1
Consider the following statements: P: Good mobile phones are not cheap Q: Cheap mobile phones are not good L: P implies Q M: Q implies P N: P is equivalent to Q Which one of the following about L, M, and N is CORRECT? Only L is TRUE. Only M is TRUE. Only N is TRUE. L, M and N are TRUE.
go_editor
asked
in
Mathematical Logic
Sep 28, 2014
by
go_editor
10.6k
views
gatecse-2014-set3
mathematical-logic
easy
propositional-logic
28
votes
6
answers
670
GATE CSE 2014 Set 2 | Question: 53
Which one of the following Boolean expressions is NOT a tautology? $((\,a\,\to\,b\,)\,\wedge\,(\,b\,\to\,c))\,\to\,(\,a\,\to\,c)$ $(\,a\,\to\,c\,)\,\to\,(\,\sim b\,\to\,(a\,\wedge\,c))$ $(\,a\,\wedge\,b\,\wedge\,c)\,\to\,(\,c\vee\,a)$ $a\,\to\,(b\,\to\,a)$
go_editor
asked
in
Mathematical Logic
Sep 28, 2014
by
go_editor
9.1k
views
gatecse-2014-set2
mathematical-logic
propositional-logic
normal
51
votes
12
answers
671
GATE CSE 2014 Set 1 | Question: 53
Which one of the following propositional logic formulas is TRUE when exactly two of $p,q$ and $r$ are TRUE? $(( p \leftrightarrow q) \wedge r) \vee (p \wedge q \wedge \sim r)$ $( \sim (p \leftrightarrow q) \wedge r)\vee (p \wedge q \wedge \sim r)$ ... $(\sim (p \leftrightarrow q) \wedge r) \wedge (p \wedge q \wedge \sim r) $
go_editor
asked
in
Mathematical Logic
Sep 28, 2014
by
go_editor
13.5k
views
gatecse-2014-set1
mathematical-logic
normal
propositional-logic
39
votes
5
answers
672
GATE CSE 1998 | Question: 1.5
What is the converse of the following assertion? I stay only if you go I stay if you go If I stay then you go If you do not go then I do not stay If I do not stay then you go
Kathleen
asked
in
Mathematical Logic
Sep 25, 2014
by
Kathleen
13.8k
views
gate1998
mathematical-logic
easy
propositional-logic
13
votes
3
answers
673
GATE CSE 1999 | Question: 14
Show that the formula $\left[(\sim p \vee q) \Rightarrow (q \Rightarrow p)\right]$ is not a tautology. Let $A$ be a tautology and $B$ any other formula. Prove that $(A \vee B)$ is a tautology.
Kathleen
asked
in
Mathematical Logic
Sep 23, 2014
by
Kathleen
2.4k
views
gate1999
mathematical-logic
normal
propositional-logic
proof
descriptive
34
votes
4
answers
674
GATE CSE 2005 | Question: 40
Let $P, Q,$ and $R$ be three atomic propositional assertions. Let $X$ denote $( P ∨ Q ) → R$ and $Y$ denote $(P → R) ∨ (Q → R).$ Which one of the following is a tautology? $X ≡ Y$ $X → Y$ $Y → X$ $¬Y → X$
gatecse
asked
in
Mathematical Logic
Sep 21, 2014
by
gatecse
6.5k
views
gatecse-2005
mathematical-logic
propositional-logic
normal
32
votes
5
answers
675
GATE CSE 2004 | Question: 70
The following propositional statement is $\left(P \implies \left(Q \vee R\right)\right) \implies \left(\left(P \wedge Q \right)\implies R\right)$ satisfiable but not valid valid a contradiction None of the above
Kathleen
asked
in
Mathematical Logic
Sep 18, 2014
by
Kathleen
7.4k
views
gatecse-2004
mathematical-logic
normal
propositional-logic
44
votes
3
answers
676
GATE CSE 2006 | Question: 27
Consider the following propositional statements: $P_1: ((A ∧ B) → C)) ≡ ((A → C) ∧ (B → C))$ $P_2: ((A ∨ B) → C)) ≡ ((A → C) ∨ (B → C))$ Which one of the following is true? $P_1$ is a tautology, but not $P_2$ $P_2$ is a tautology, but not $P_1$ $P_1$ and $P_2$ are both tautologies Both $P_1$ and $P_2$ are not tautologies
Rucha Shelke
asked
in
Mathematical Logic
Sep 18, 2014
by
Rucha Shelke
8.4k
views
gatecse-2006
mathematical-logic
normal
propositional-logic
57
votes
6
answers
677
GATE CSE 2003 | Question: 72
The following resolution rule is used in logic programming. Derive clause $(P \vee Q)$ from clauses $(P\vee R),(Q \vee ¬R)$ Which of the following statements related to this rule is FALSE? $((P ∨ R)∧(Q ∨ ¬R))⇒(P ∨ Q)$ ... if $(P ∨ R)∧(Q ∨ ¬R)$ is satisfiable $(P ∨ Q)⇒ \text{FALSE}$ if and only if both $P$ and $Q$ are unsatisfiable
Kathleen
asked
in
Mathematical Logic
Sep 17, 2014
by
Kathleen
14.1k
views
gatecse-2003
mathematical-logic
normal
propositional-logic
57
votes
6
answers
678
GATE CSE 2003 | Question: 31
Let $(S, \leq)$ be a partial order with two minimal elements a and b, and a maximum element c. Let P: S \(\to\) {True, False} be a predicate defined on S. Suppose that P(a) = True, P(b) = False and P(x) \(\implies\) P(y) for all $x, y \in S$ satisfying $x \leq y$ ... for all x \(\in\) S such that b ≤ x and x ≠ c P(x) = False for all x \(\in\) S such that a ≤ x and b ≤ x
Kathleen
asked
in
Set Theory & Algebra
Sep 16, 2014
by
Kathleen
11.7k
views
gatecse-2003
set-theory&algebra
partial-order
normal
propositional-logic
62
votes
10
answers
679
GATE CSE 2002 | Question: 1.8
"If $X$ then $Y$ unless $Z$" is represented by which of the following formulas in propositional logic? ("$\neg$" is negation, "$\land$" is conjunction, and "$\rightarrow$" is implication) $(X\land \neg Z) \rightarrow Y$ $(X \land Y) \rightarrow \neg Z$ $X \rightarrow(Y\land \neg Z)$ $(X \rightarrow Y)\land \neg Z$
Kathleen
asked
in
Mathematical Logic
Sep 15, 2014
by
Kathleen
14.7k
views
gatecse-2002
mathematical-logic
normal
propositional-logic
33
votes
8
answers
680
GATE CSE 2009 | Question: 24
The binary operation $\Box$ ... following is equivalent to $P \vee Q$? $\neg Q \Box \neg P$ $P\Box \neg Q$ $\neg P\Box Q$ $\neg P\Box \neg Q$
gatecse
asked
in
Mathematical Logic
Sep 15, 2014
by
gatecse
8.5k
views
gatecse-2009
mathematical-logic
easy
propositional-logic
30
votes
5
answers
681
GATE CSE 2001 | Question: 1.3
Consider two well-formed formulas in propositional logic $F_1: P \Rightarrow \neg P$ $F_2: (P \Rightarrow \neg P) \lor ( \neg P \Rightarrow P)$ Which one of the following statements is correct? $F_1$ is satisfiable, $F_2$ is valid $F_1$ unsatisfiable, $F_2$ is satisfiable $F_1$ is unsatisfiable, $F_2$ is valid $F_1$ and $F_2$ are both satisfiable
Kathleen
asked
in
Mathematical Logic
Sep 14, 2014
by
Kathleen
9.0k
views
gatecse-2001
mathematical-logic
easy
propositional-logic
47
votes
7
answers
682
GATE CSE 2000 | Question: 2.7
Let $a, b, c, d$ be propositions. Assume that the equivalence $a ⇔ ( b \vee \neg b)$ and $b ⇔c$ hold. Then the truth-value of the formula $(a ∧ b) → (a ∧ c) ∨ d$ is always True False Same as the truth-value of $b$ Same as the truth-value of $d$
Kathleen
asked
in
Mathematical Logic
Sep 14, 2014
by
Kathleen
12.1k
views
gatecse-2000
mathematical-logic
normal
propositional-logic
12
votes
1
answer
683
GATE CSE 1992 | Question: 15.a
Use Modus ponens $(A, A → B |= B)$ or resolution to show that the following set is inconsistent: $Q(x) \rightarrow P (x) \vee \sim R (a)$ $R (a) \vee \sim Q(a)$ $Q(a)$ $\sim P (y)$ where $x$ and $y$ are universally quantified variables, $a$ is a constant and $P, Q, R$ are monadic predicates.
Kathleen
asked
in
Mathematical Logic
Sep 13, 2014
by
Kathleen
3.3k
views
gate1992
normal
mathematical-logic
propositional-logic
descriptive
24
votes
4
answers
684
GATE CSE 1992 | Question: 02,xvi
Which of the following is/are a tautology? $a \vee b \to b \wedge c$ $a \wedge b \to b \vee c$ $a \vee b \to \left(b \to c \right)$ $a \to b \to \left(b \to c \right)$
Kathleen
asked
in
Mathematical Logic
Sep 13, 2014
by
Kathleen
9.7k
views
gate1992
mathematical-logic
easy
propositional-logic
multiple-selects
39
votes
9
answers
685
GATE CSE 1991 | Question: 03,xii
If $F_1$, $F_2$ and $F_3$ are propositional formulae such that $F_1 \land F_2 \rightarrow F_3$ and $F_1 \land F_2 \rightarrow \sim F_3$ are both tautologies, then which of the following is true: Both $F_1$ and $F_2$ are tautologies The conjunction $F_1 \land F_2$ is not satisfiable Neither is tautologous Neither is satisfiable None of the above
Kathleen
asked
in
Mathematical Logic
Sep 12, 2014
by
Kathleen
8.8k
views
gate1991
mathematical-logic
normal
propositional-logic
multiple-selects
30
votes
7
answers
686
GATE CSE 2008 | Question: 31
$P$ and $Q$ are two propositions. Which of the following logical expressions are equivalent? $P ∨ \neg Q$ $\neg(\neg P ∧ Q)$ $(P ∧ Q) ∨ (P ∧ \neg Q) ∨ (\neg P ∧ \neg Q)$ $(P ∧ Q) ∨ (P ∧ \neg Q) ∨ (\neg P ∧ Q)$ Only I and II Only I, II and III Only I, II and IV All of I, II, III and IV
Kathleen
asked
in
Mathematical Logic
Sep 12, 2014
by
Kathleen
8.4k
views
gatecse-2008
normal
mathematical-logic
propositional-logic
19
votes
5
answers
687
TIFR CSE 2011 | Part A | Question: 1
If either wages or prices are raised, there will be inflation. If there is inflation, then either the government must regulate it or the people will suffer. If the people suffer, the government will be unpopular. Government will not be ... raised Prices are not raised If the inflation is not regulated, then the prices are not raised Wages are not raised
Marv Patel
asked
in
Mathematical Logic
Aug 31, 2014
by
Marv Patel
2.9k
views
tifr2011
mathematical-logic
propositional-logic
normal
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