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Search results for propositional-logic
100
votes
11
answers
1
GATE CSE 2016 Set 2 | Question: 01
Consider the following expressions: $false$ $Q$ $true$ $P\vee Q$ $\neg Q\vee P$ The number of expressions given above that are logically implied by $P \wedge (P \Rightarrow Q)$ is ___________.
Consider the following expressions:$false$$Q$$true$$P\vee Q$$\neg Q\vee P$The number of expressions given above that are logically implied by $P \wedge (P \Rightarrow Q)$...
Akash Kanase
19.7k
views
Akash Kanase
asked
Feb 12, 2016
Mathematical Logic
gatecse-2016-set2
mathematical-logic
normal
numerical-answers
propositional-logic
+
–
71
votes
7
answers
2
GATE CSE 2016 Set 1 | Question: 1
Let $p, q, r, s$ represents the following propositions. $p:x\in\left\{8, 9, 10, 11, 12\right\}$ $q:$ $x$ is a composite number. $r:$ $x$ is a perfect square. $s:$ $x$ is a prime number. The integer $x\geq2$ which satisfies $\neg\left(\left(p\Rightarrow q\right) \wedge \left(\neg r \vee \neg s\right)\right)$ is ____________.
Let $p, q, r, s$ represents the following propositions.$p:x\in\left\{8, 9, 10, 11, 12\right\}$$q:$ $x$ is a composite number.$r:$ $x$ is a perfect square.$s:$ $x$ is a pr...
Sandeep Singh
12.9k
views
Sandeep Singh
asked
Feb 12, 2016
Mathematical Logic
gatecse-2016-set1
mathematical-logic
normal
numerical-answers
propositional-logic
+
–
62
votes
10
answers
3
GATE CSE 2002 | Question: 1.8
"If $X$ then $Y$ unless $Z$" is represented by which of the following formulas in propositional logic? ("$\neg$" is negation, "$\land$" is conjunction, and "$\rightarrow$" is implication) $(X\land \neg Z) \rightarrow Y$ $(X \land Y) \rightarrow \neg Z$ $X \rightarrow(Y\land \neg Z)$ $(X \rightarrow Y)\land \neg Z$
"If $X$ then $Y$ unless $Z$" is represented by which of the following formulas in propositional logic? ("$\neg$" is negation, "$\land$" is conjunction, and "$\rightarrow$...
Kathleen
14.6k
views
Kathleen
asked
Sep 15, 2014
Mathematical Logic
gatecse-2002
mathematical-logic
normal
propositional-logic
+
–
14
votes
8
answers
4
GATE CSE 2021 Set 1 | Question: 7
Let $p$ and $q$ be two propositions. Consider the following two formulae in propositional logic. $S_1: (\neg p\wedge(p\vee q))\rightarrow q$ $S_2: q\rightarrow(\neg p\wedge(p\vee q))$ Which one of the following choices is correct? Both $S_1$ and ... but $S_2$ is not a tautology $S_1$ is not a tautology but $S_2$ is a tautology Neither $S_1$ nor $S_2$ is a tautology
Let $p$ and $q$ be two propositions. Consider the following two formulae in propositional logic.$S_1: (\neg p\wedge(p\vee q))\rightarrow q$$S_2: q\rightarrow(\neg p\wedge...
Arjun
8.1k
views
Arjun
asked
Feb 18, 2021
Mathematical Logic
gatecse-2021-set1
mathematical-logic
propositional-logic
1-mark
+
–
27
votes
9
answers
5
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
8.7k
views
Arjun
asked
Feb 18, 2021
Mathematical Logic
gatecse-2021-set2
multiple-selects
mathematical-logic
propositional-logic
1-mark
+
–
57
votes
10
answers
6
GATE CSE 2017 Set 2 | Question: 11
Let $p, q, r$ ... $(\neg p \wedge r) \vee (r \rightarrow (p \wedge q))$
Let $p, q, r$ denote the statements ”It is raining”, “It is cold”, and “It is pleasant”, respectively. Then the statement “It is not raining and it is pleas...
khushtak
12.1k
views
khushtak
asked
Feb 14, 2017
Mathematical Logic
gatecse-2017-set2
mathematical-logic
propositional-logic
+
–
51
votes
12
answers
7
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) $
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...
go_editor
13.4k
views
go_editor
asked
Sep 28, 2014
Mathematical Logic
gatecse-2014-set1
mathematical-logic
normal
propositional-logic
+
–
39
votes
5
answers
8
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
What is the converse of the following assertion?I stay only if you goI stay if you goIf I stay then you goIf you do not go then I do not stayIf I do not stay then you go
Kathleen
13.8k
views
Kathleen
asked
Sep 25, 2014
Mathematical Logic
gate1998
mathematical-logic
easy
propositional-logic
+
–
48
votes
10
answers
9
GATE CSE 2017 Set 1 | Question: 29
Let $p$, $q$ and $r$ be propositions and the expression $\left ( p\rightarrow q \right )\rightarrow r$ be a contradiction. Then, the expression $\left ( r\rightarrow p \right )\rightarrow q$ is a tautology a contradiction always TRUE when $p$ is FALSE always TRUE when $q$ is TRUE
Let $p$, $q$ and $r$ be propositions and the expression $\left ( p\rightarrow q \right )\rightarrow r$ be a contradiction. Then, the expression $\left ( r\rightarrow p \r...
Arjun
10.5k
views
Arjun
asked
Feb 14, 2017
Mathematical Logic
gatecse-2017-set1
mathematical-logic
propositional-logic
+
–
57
votes
6
answers
10
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
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(...
Kathleen
11.6k
views
Kathleen
asked
Sep 16, 2014
Set Theory & Algebra
gatecse-2003
set-theory&algebra
partial-order
normal
propositional-logic
+
–
57
votes
6
answers
11
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
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 th...
Kathleen
13.9k
views
Kathleen
asked
Sep 17, 2014
Mathematical Logic
gatecse-2003
mathematical-logic
normal
propositional-logic
+
–
47
votes
7
answers
12
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 $d$
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) ∨...
Kathleen
12.0k
views
Kathleen
asked
Sep 14, 2014
Mathematical Logic
gatecse-2000
mathematical-logic
normal
propositional-logic
+
–
53
votes
5
answers
13
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.
Consider the following statements:P: Good mobile phones are not cheapQ: Cheap mobile phones are not goodL: P implies QM: Q implies PN: P is equivalent to QWhich one of th...
go_editor
10.5k
views
go_editor
asked
Sep 28, 2014
Mathematical Logic
gatecse-2014-set3
mathematical-logic
easy
propositional-logic
+
–
29
votes
6
answers
14
GATE CSE 1990 | Question: 3-x
Indicate which of the following well-formed formulae are valid: $\left(P\Rightarrow Q\right) {\wedge} \left(Q \Rightarrow R\right) \Rightarrow \left(P \Rightarrow R\right)$ ...
Indicate which of the following well-formed formulae are valid:$\left(P\Rightarrow Q\right) {\wedge} \left(Q \Rightarrow R\right) \Rightarrow \left(P \Rightarrow R\right)...
makhdoom ghaya
9.2k
views
makhdoom ghaya
asked
Nov 22, 2016
Mathematical Logic
gate1990
normal
mathematical-logic
propositional-logic
multiple-selects
+
–
41
votes
9
answers
15
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 $S$
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)$$Q: [(¬p ∧q) �...
Ishrat Jahan
11.7k
views
Ishrat Jahan
asked
Nov 2, 2014
Mathematical Logic
gateit-2004
mathematical-logic
normal
propositional-logic
+
–
29
votes
8
answers
16
GATE CSE 2017 Set 1 | Question: 01
The statement $\left ( ¬p \right ) \Rightarrow \left ( ¬q \right )$ is logically equivalent to which of the statements below? $p \Rightarrow q$ $q \Rightarrow p$ $\left ( ¬q \right ) \vee p$ $\left ( ¬p \right ) \vee q$ I only I and IV only II only II and III only
The statement $\left ( ¬p \right ) \Rightarrow \left ( ¬q \right )$ is logically equivalent to which of the statements below?$p \Rightarrow q$$q \Rightarrow p$$\left ( ...
khushtak
8.9k
views
khushtak
asked
Feb 14, 2017
Mathematical Logic
gatecse-2017-set1
mathematical-logic
propositional-logic
easy
+
–
40
votes
9
answers
17
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
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 ...
Kathleen
8.6k
views
Kathleen
asked
Sep 12, 2014
Mathematical Logic
gate1991
mathematical-logic
normal
propositional-logic
multiple-selects
+
–
11
votes
2
answers
18
GO Classes Test Series 2024 | Mock GATE | Test 14 | Question: 58
Let $\mathrm{F}$ and $\mathrm{G}$ be two propositional formulae. Which of the following is/are True? If $F \vee G$ is a tautology then at least one of $F, G$ is a tautology. If $F \wedge G$ is a contradiction then at ... $G$ is a tautology. If $F \rightarrow G$ is a contradiction then $F$ is a tautology and $G$ is a contradiction.
Let $\mathrm{F}$ and $\mathrm{G}$ be two propositional formulae.Which of the following is/are True?If $F \vee G$ is a tautology then at least one of $F, G$ is a tautology...
GO Classes
728
views
GO Classes
asked
Feb 5
Mathematical Logic
goclasses2024-mockgate-14
mathematical-logic
propositional-logic
multiple-selects
2-marks
+
–
0
votes
1
answer
19
Does Either...Or means Exclusive Or or Inclusive Or?
Let's take a compound propositions Either it is below freezing or it is snowing. Now if $p$: it is below freezing $q$: it is snowing Will it be $p \vee q$ or $p \oplus q$? There are some instances where semantics are ... both cases can't be true, because if you are ill you can't appear for example and you must be in one state.
Let's take a compound propositionsEither it is below freezing or it is snowing.Now if$p$: it is below freezing $q$: it is snowingWill it be $p \vee q$ or $p \oplus q$? Th...
tbhaxor
102
views
tbhaxor
asked
Mar 12
Mathematical Logic
propositional-logic
mathematical-logic
+
–
1
votes
1
answer
20
Why (p ∨ T) is not a tautology?
tbhaxor
141
views
tbhaxor
asked
Mar 5
Mathematical Logic
mathematical-logic
propositional-logic
+
–
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