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Recent questions tagged propositional-logic
0
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19
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kenneth h rosen chapter 1 section section 1.5 nested quatnifiers excercise 49
ykrishnay
asked
in
Mathematical Logic
Apr 20
by
ykrishnay
103
points
19
views
kenneth-rosen
combinatory
mathematical-logic
discrete-mathematics
propositional-logic
0
votes
0
answers
7
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kenneth h rosen chapter 1 section "Nested quantifers" excercise 1.5 question 26's g
ykrishnay
asked
in
Mathematical Logic
Apr 18
by
ykrishnay
103
points
7
views
kenneth-rosen
combinatory
mathematical-logic
propositional-logic
discrete-mathematics
0
votes
0
answers
6
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kenneth h rosen chapter 1 section 1.5 excercise 1.5 question 18 e
ykrishnay
asked
in
Mathematical Logic
Apr 16
by
ykrishnay
103
points
6
views
kenneth-rosen
combinatory
mathematical-logic
propositional-logic
discrete-mathematics
0
votes
0
answers
19
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Kenneth h rosen chapter 1 section 1.5 question 8
Let Q(x, y) be the statement student x has been a con- testant on quiz show y. Express each of these sentences in terms of Q(x, y), quantifiers, and logical connectives, where the domain for x consists of all students at ... a student from your school as a contestant. e) At least two students from your school have been con- testants on Jeopardy.
ykrishnay
asked
in
Mathematical Logic
Apr 12
by
ykrishnay
103
points
19
views
kenneth-rosen
discrete-mathematics
combinatory
mathematical-logic
propositional-logic
0
votes
0
answers
42
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kenneth h rosen chapter 1 excercise 1.4 predicates and quantifiers question 46
ykrishnay
asked
in
Mathematical Logic
Mar 20
by
ykrishnay
103
points
42
views
kenneth-rosen
combinatory
mathematical-logic
propositional-logic
0
votes
0
answers
19
views
kenneth h rosen chapter 1 excercise 1.4 predicates and quantifiers question 33
ykrishnay
asked
in
Mathematical Logic
Mar 19
by
ykrishnay
103
points
19
views
discrete-mathematics
kenneth-rosen
combinatory
propositional-logic
mathematical-logic
0
votes
0
answers
27
views
kenneth h rosen chapter 1 excercise 1.4 predicated and quantifiers question 19
ykrishnay
asked
in
Mathematical Logic
Mar 18
by
ykrishnay
103
points
27
views
discrete-mathematics
kenneth-rosen
combinatory
propositional-logic
mathematical-logic
0
votes
0
answers
26
views
Kenneth h rosen chapter 1 section 1.4 binding variables
ykrishnay
asked
in
Mathematical Logic
Mar 15
by
ykrishnay
103
points
26
views
discrete-mathematics
kenneth-rosen
mathematical-logic
propositional-logic
combinatory
0
votes
0
answers
57
views
kenneth h rosen chapter 1 excercise 1.2
hey i want to ask that in excercise 1.2 there are lots of logic puzzles quetions so it is important for gate or any exam like gate can i leave those questions or do ? please tell need an answer.
ykrishnay
asked
in
Mathematical Logic
Feb 17
by
ykrishnay
103
points
57
views
discrete-mathematics
kenneth-rosen
combinatory
propositional-logic
mathematical-logic
0
votes
0
answers
47
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kenneth h rosen chapter 1 excercise 1.2 question 15 on page 23
ykrishnay
asked
in
Mathematical Logic
Feb 17
by
ykrishnay
103
points
47
views
discrete-mathematics
kenneth-rosen
propositional-logic
combinatory
mathematical-logic
0
votes
0
answers
44
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kenneth h rosen chapter-1 section 1.1 propsitional logic excercise 1.1 question 23's d) and e)
ykrishnay
asked
in
Mathematical Logic
Feb 13
by
ykrishnay
103
points
44
views
discrete-mathematics
kenneth-rosen
combinatory
mathematical-logic
propositional-logic
1
vote
1
answer
95
views
Discrete mathematics Kenneth Rosen The foundation logic and proofs page 22 question 4
abh01032001
asked
in
Mathematical Logic
Aug 18, 2021
by
abh01032001
9
points
95
views
discrete-mathematics
kenneth-rosen
propositional-logic
0
votes
0
answers
35
views
Discrete Mathematics
How to prove the following statement is valid with the help of Inference Rules? (P $\wedge$ ( P $\rightarrow$ Q) ) $\rightarrow$ ($\sim$ Q $\vee$ P)
ShivangiChauhan
asked
in
Mathematical Logic
Jul 27, 2021
by
ShivangiChauhan
17
points
35
views
self-doubt
discrete-mathematics
propositional-logic
3
votes
3
answers
725
views
GATE CSE 2021 Set 2 | Question: 15 | Video Solution
Arjun
asked
in
Mathematical Logic
Feb 18, 2021
by
Arjun
1.4k
points
725
views
gate2021-cse-set2
multiple-selects
mathematical-logic
propositional-logic
1
vote
4
answers
520
views
GATE CSE 2021 Set 1 | Question: 7 | Video Solution
Arjun
asked
in
Mathematical Logic
Feb 18, 2021
by
Arjun
1.4k
points
520
views
gate2021-cse-set1
mathematical-logic
propositional-logic
0
votes
0
answers
23
views
GATE2016-2-01 Video Solution
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 ___________.
admin
asked
in
Mathematical Logic
Apr 18, 2020
by
admin
585
points
23
views
gate2016-2
mathematical-logic
normal
numerical-answers
propositional-logic
video-solution
0
votes
0
answers
26
views
GATE2016-1-1 Video Solution
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 ____________.
admin
asked
in
Mathematical Logic
Apr 18, 2020
by
admin
585
points
26
views
gate2016-1
mathematical-logic
normal
numerical-answers
propositional-logic
video-solution
0
votes
0
answers
23
views
GATE2002-1.8 Video Solution
"If $X$ then $Y$ unless $Z$" is represented by which of the following formulas in prepositional logic? ("$\neg$" is negation, "$\land$" is conjunction, and "$\rightarrow$" is implication) $(X\land \neg Z) \rightarrow Y$ $(X \land Y) \rightarrow \neg Z$ $X \rightarrow(Y\land \neg Z)$ $(X \rightarrow Y)\land \neg Z$
admin
asked
in
Mathematical Logic
Apr 18, 2020
by
admin
585
points
23
views
gate2002
mathematical-logic
normal
propositional-logic
video-solution
0
votes
0
answers
24
views
GATE2017-2-11 Video Solution
Let $p, q, r$ ... $(\neg p \wedge r) \vee (r \rightarrow (p \wedge q))$
admin
asked
in
Mathematical Logic
Apr 18, 2020
by
admin
585
points
24
views
gate2017-2
mathematical-logic
propositional-logic
video-solution
0
votes
0
answers
16
views
GATE2014-1-53 Video Solution
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) $
admin
asked
in
Mathematical Logic
Apr 18, 2020
by
admin
585
points
16
views
gate2014-1
mathematical-logic
normal
propositional-logic
video-solution
0
votes
0
answers
22
views
GATE1998-1.5 Video Solution
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
admin
asked
in
Mathematical Logic
Apr 18, 2020
by
admin
585
points
22
views
gate1998
mathematical-logic
easy
propositional-logic
video-solution
0
votes
0
answers
18
views
GATE2003-72 Video Solution
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? $((P ∨ R)∧(Q ∨ ¬R))⇒(P ∨ Q)$ ... only if $(P ∨ R)∧(Q ∨ ¬R)$ is satisfiable $(P ∨ Q)⇒ \text{FALSE}$ if and only if both $P$ and $Q$ are unsatisfiable
admin
asked
in
Mathematical Logic
Apr 18, 2020
by
admin
585
points
18
views
gate2003
mathematical-logic
normal
propositional-logic
video-solution
0
votes
0
answers
18
views
GATE2017-1-29 Video Solution
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
admin
asked
in
Mathematical Logic
Apr 18, 2020
by
admin
585
points
18
views
gate2017-1
mathematical-logic
propositional-logic
video-solution
0
votes
0
answers
45
views
GATE2003-31 Video Solution
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
admin
asked
in
Set Theory & Algebra
Apr 18, 2020
by
admin
585
points
45
views
gate2003
set-theory&algebra
partial-order
normal
propositional-logic
video-solution
0
votes
0
answers
15
views
GATE2017-1-01 Video Solution
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
admin
asked
in
Mathematical Logic
Apr 18, 2020
by
admin
585
points
15
views
gate2017-1
mathematical-logic
propositional-logic
easy
video-solution
0
votes
0
answers
21
views
GATE2014-3-1 Video Solution
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.
admin
asked
in
Mathematical Logic
Apr 18, 2020
by
admin
585
points
21
views
gate2014-3
mathematical-logic
easy
propositional-logic
video-solution
0
votes
0
answers
19
views
GATE2004-IT-31 Video Solution
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 $S$
admin
asked
in
Mathematical Logic
Apr 18, 2020
by
admin
585
points
19
views
gate2004-it
mathematical-logic
normal
propositional-logic
video-solution
0
votes
0
answers
19
views
GATE2014-2-53 Video Solution
Which one of the following Boolean expressions is NOT a tautology? $((\,a\,\to\,b\,)\,\wedge\,(\,b\,\to\,c))\,\to\,(\,a\,\to\,c)$ $(\,a\,\to\,c\,)\,\to\,(\,\sim b\,\to\,(a\,\wedge\,c))$ $(\,a\,\wedge\,b\,\wedge\,c)\,\to\,(\,c\vee\,a)$ $a\,\to\,(b\,\to\,a)$
admin
asked
in
Mathematical Logic
Apr 18, 2020
by
admin
585
points
19
views
gate2014-2
mathematical-logic
propositional-logic
normal
video-solution
0
votes
0
answers
21
views
GATE2000-2.7 Video Solution
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 $d$
admin
asked
in
Mathematical Logic
Apr 18, 2020
by
admin
585
points
21
views
gate2000
mathematical-logic
normal
propositional-logic
video-solution
0
votes
0
answers
22
views
GATE2001-1.3 Video Solution
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
admin
asked
in
Mathematical Logic
Apr 18, 2020
by
admin
585
points
22
views
gate2001
mathematical-logic
easy
propositional-logic
video-solution
0
votes
0
answers
18
views
GATE2015-1-14 Video Solution
Which one of the following is NOT equivalent to $p ↔ q$? $(\neg p ∨ q) ∧ (p ∨ \neg q)$ $(\neg p ∨ q) ∧ (q → p)$ $(\neg p ∧ q) ∨ ( p ∧ \neg q)$ $(\neg p ∧ \neg q) ∨ (p ∧ q)$
admin
asked
in
Mathematical Logic
Apr 18, 2020
by
admin
585
points
18
views
gate2015-1
mathematical-logic
easy
propositional-logic
video-solution
0
votes
0
answers
12
views
GATE1995-2.19 Video Solution
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
admin
asked
in
Mathematical Logic
Apr 18, 2020
by
admin
585
points
12
views
gate1995
mathematical-logic
normal
propositional-logic
video-solution
0
votes
0
answers
12
views
GATE2006-27 Video Solution
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
admin
asked
in
Mathematical Logic
Apr 18, 2020
by
admin
585
points
12
views
gate2006
mathematical-logic
normal
propositional-logic
video-solution
0
votes
0
answers
16
views
GATE2009-24 Video Solution
The binary operation $\Box$ ... following is equivalent to $P \vee Q$? $\neg Q \Box \neg P$ $P\Box \neg Q$ $\neg P\Box Q$ $\neg P\Box \neg Q$
admin
asked
in
Mathematical Logic
Apr 18, 2020
by
admin
585
points
16
views
gate2009
mathematical-logic
easy
propositional-logic
video-solution
0
votes
0
answers
18
views
GATE2008-31 Video Solution
$P$ 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
admin
asked
in
Mathematical Logic
Apr 18, 2020
by
admin
585
points
18
views
gate2008
normal
mathematical-logic
propositional-logic
video-solution
0
votes
0
answers
16
views
GATE2004-70 Video Solution
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
admin
asked
in
Mathematical Logic
Apr 18, 2020
by
admin
585
points
16
views
gate2004
mathematical-logic
normal
propositional-logic
video-solution
0
votes
0
answers
16
views
GATE1990-3-x Video Solution
Choose the correct alternatives (More than one may be correct). Indicate which of the following well-formed formulae are valid: $\left(P\Rightarrow Q\right) {\wedge} \left(Q \Rightarrow R\right) \Rightarrow \left(P \Rightarrow R\right)$ ...
admin
asked
in
Mathematical Logic
Apr 18, 2020
by
admin
585
points
16
views
gate1990
normal
mathematical-logic
propositional-logic
video-solution
0
votes
0
answers
17
views
GATE2005-40 Video Solution
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? $X ≡ Y$ $X → Y$ $Y → X$ $¬Y → X$
admin
asked
in
Mathematical Logic
Apr 18, 2020
by
admin
585
points
17
views
gate2005
mathematical-logic
propositional-logic
normal
video-solution
0
votes
0
answers
14
views
GATE1996-2.3 Video Solution
Which of the following is false? Read $\wedge$ as AND, $\vee$ as OR, $\neg$ as NOT, $\rightarrow$ as one way implication and $\leftrightarrow$ as two way implication $((x \rightarrow y) \wedge x) \rightarrow y$ ... $(x \rightarrow (x \vee y))$ $((x \vee y) \leftrightarrow (\neg x \rightarrow \neg y))$
admin
asked
in
Mathematical Logic
Apr 18, 2020
by
admin
585
points
14
views
gate1996
mathematical-logic
normal
propositional-logic
video-solution
0
votes
0
answers
22
views
GATE1991-03,xii Video Solution
Choose the correct alternatives (more than one may be correct) and write the corresponding letters only: If $F_1$, $F_2$ and $F_3$ are propositional formulae such that $F_1 \land F_2 \rightarrow F_3$ ... $F_1 \land F_2$ is not satisfiable Neither is tautologous Neither is satisfiable None of the above.
admin
asked
in
Mathematical Logic
Apr 18, 2020
by
admin
585
points
22
views
gate1991
mathematical-logic
normal
propositional-logic
video-solution
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