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Recent questions tagged mathematical-logic

Recent questions tagged mathematical-logic
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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
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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
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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
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0 answers 19 views
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
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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
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0 answers 44 views
kenneth h rosen chapter 1 excercise 1.4 predicates ad quantifiers question 59 symbolic logic
ykrishnay asked in Mathematical Logic Mar 19
by ykrishnay
103 points
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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
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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
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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
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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
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0 answers 47 views
kenneth h rosen chapter 1 excercise 1.2 question 15 on page 23
ykrishnay asked in Mathematical Logic Feb 17
by ykrishnay
103 points
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0 votes
0 answers 44 views
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
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0 answers 18 views
#probability
I have a bag containing 20 red balls and 16 blue balls. I uniformly randomly take balls out from the bag without replacement until all balls of color have been removed. If the probability that the last ball I took was red can be represented as p/q , where p and q ... of drawing all the balls is 36c20. The probability is 35c19/36c20=5/9. but the answer is 4/9. pls, correct my solution?
DEBANJAN GHOSH asked in Mathematical Logic Jun 26, 2021
by DEBANJAN GHOSH
5 points
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0 answers 35 views
Boolean algebra. Complementation of variables
In boolean logic(DLD) do we always consider a complemented variable as false and a non complemented variable as True? Also while solving problems, can we assume any non complemented variable as 0 and solve? Any help is grealty appreciated (For solving problems in Digital Logic)
Pranavapp asked in Digital Logic Jul 13, 2020
by Pranavapp
5 points
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0 answers 33 views
GATE2018-28 Video Solution
Consider the first-order logic sentence $\varphi \equiv \exists \: s \: \exists \: t \: \exists \: u \: \forall \: v \: \forall \: w \forall \: x \: \forall \: y \: \psi(s, t, u, v, w, x, y)$ ... or equal to $3$ There exists no model of $\varphi$ with universe size of greater than $7$ Every model of $\varphi$ has a universe of size equal to $7$
admin asked in Mathematical Logic Apr 18, 2020
by admin
585 points
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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
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GATE2015-2-55 Video Solution
Which one of the following well-formed formulae is a tautology? $\forall x \, \exists y \, R(x,y) \, \leftrightarrow \, \exists y \, \forall x \, R(x, y)$ ... $\forall x \, \forall y \, P(x,y) \, \rightarrow \, \forall x \, \forall y \, P(y, x)$
admin asked in Mathematical Logic Apr 18, 2020
by admin
585 points
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0 answers 28 views
GATE2019-35 Video Solution
Consider the first order predicate formula $\varphi$: $\forall x [ ( \forall z \: z \mid x \Rightarrow (( z=x) \vee (z=1))) \rightarrow \exists w ( w > x) \wedge (\forall z \: z \mid w \Rightarrow ((w=z) \vee (z=1)))]$ ... of all positive integers $S3:$ Set of all integers Which of the above sets satisfy $\varphi$? S1 and S2 S1 and S3 S2 and S3 S1, S2 and S3
admin asked in Mathematical Logic Apr 18, 2020
by admin
585 points
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0 answers 22 views
GATE2016-2-27 Video Solution
Which one of the following well-formed formulae in predicate calculus is NOT valid ? $(\forall _{x} p(x) \implies \forall _{x} q(x)) \implies (\exists _{x} \neg p(x) \vee \forall _{x} q(x))$ ... $\forall x (p(x) \vee q(x)) \implies (\forall x p(x) \vee \forall x q(x))$
admin asked in Mathematical Logic Apr 18, 2020
by admin
585 points
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0 answers 29 views
GATE2017-1-02 Video Solution
Consider the first-order logic sentence $F:\forall x(\exists yR(x,y))$. Assuming non-empty logical domains, which of the sentences below are implied by $F$? $\exists y(\exists xR(x,y))$ $\exists y(\forall xR(x,y))$ $\forall y(\exists xR(x,y))$ $¬\exists x(\forall y¬R(x,y))$ IV only I and IV only II only II and III only
admin asked in Mathematical Logic Apr 18, 2020
by admin
585 points
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1 vote
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GATE2003-32 Video Solution
Which of the following is a valid first order formula? (Here \(\alpha\) and \(\beta\) are first order formulae with $x$ as their only free variable) $((∀x)[α] ⇒ (∀x)[β]) ⇒ (∀x)[α ⇒ β]$ $(∀x)[α] ⇒ (∃x)[α ∧ β]$ $((∀x)[α ∨ β] ⇒ (∃x)[α]) ⇒ (∀x)[α]$ $(∀x)[α ⇒ β] ⇒ (((∀x)[α]) ⇒ (∀x)[β])$
admin asked in Mathematical Logic Apr 18, 2020
by admin
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GATE2015-3-24 Video Solution
In a room there are only two types of people, namely $\text{Type 1}$ and $\text{Type 2}$. $\text{Type 1}$ people always tell the truth and $\text{Type 2}$ people always lie. You give a fair coin to a person in that room, without knowing which type he ... person is of $\text{Type 2}$, then the result is tail If the person is of $\text{Type 1}$, then the result is tail
admin asked in Mathematical Logic Apr 18, 2020
by admin
585 points
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0 answers 26 views
GATE1992-92,xv Video Solution
Which of the following predicate calculus statements is/are valid? $(\forall (x)) P(x) \vee (\forall(x))Q(x) \implies (\forall (x)) (P(x) \vee Q(x))$ $(\exists (x)) P(x) \wedge (\exists (x))Q(x) \implies (\exists (x)) (P(x) \wedge Q(x))$ ... $(\exists (x)) (P(x) \vee Q(x)) \implies \sim (\forall (x)) P(x) \vee (\exists (x)) Q(x)$
admin asked in Mathematical Logic Apr 18, 2020
by admin
585 points
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GATE2004-23, ISRO2007-32 Video Solution
Identify the correct translation into logical notation of the following assertion. Some boys in the class are taller than all the girls Note: $\text{taller} (x, y)$ is true if $x$ is taller than $y$ ... $(\exists x) (\text{boy}(x) \land (\forall y) (\text{girl}(y) \rightarrow \text{taller}(x, y)))$
admin asked in Mathematical Logic Apr 18, 2020
by admin
585 points
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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
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GATE2010-30 Video Solution
Suppose the predicate $F(x, y, t)$ is used to represent the statement that person $x$ can fool person $y$ at time $t$. Which one of the statements below expresses best the meaning of the formula, $\qquad∀x∃y∃t(¬F(x,y,t))$ Everyone can fool ... time No one can fool everyone all the time Everyone cannot fool some person all the time No one can fool some person at some time
admin asked in Mathematical Logic Apr 18, 2020
by admin
585 points
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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
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GATE2003-33 Video Solution
Consider the following formula and its two interpretations \(I_1\) and \(I_2\). \(\alpha: (\forall x)\left[P_x \Leftrightarrow (\forall y)\left[Q_{xy} \Leftrightarrow \neg Q_{yy} \right]\right] \Rightarrow (\forall x)\left[\neg P_x\right]\) \(I_1\) : Domain: ... (I_1\) does not Neither \(I_1\) nor \(I_2\) satisfies \(\alpha\) Both \(I_1\) and \(I_2\) satisfies \(\alpha\)
admin asked in Mathematical Logic Apr 18, 2020
by admin
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GATE2005-IT-36 Video Solution
Let $P(x)$ and $Q(x)$ ...
admin asked in Mathematical Logic Apr 18, 2020
by admin
585 points
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0 answers 11 views
GATE2006-IT-21 Video Solution
Consider the following first order logic formula in which $R$ is a binary relation symbol. $∀x∀y (R(x, y) \implies R(y, x))$ The formula is satisfiable and valid satisfiable and so is its negation unsatisfiable but its negation is valid satisfiable but its negation is unsatisfiable
admin asked in Mathematical Logic Apr 18, 2020
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585 points
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0 answers 30 views
GATE2008-30 Video Solution
Let $\text{fsa}$ and $\text{pda}$ be two predicates such that $\text{fsa}(x)$ means $x$ is a finite state automaton and $\text{pda}(y)$ means that $y$ is a pushdown automaton. Let $\text{equivalent}$ ...
admin asked in Mathematical Logic Apr 18, 2020
by admin
585 points
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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
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GATE2011-30 Video Solution
Which one of the following options is CORRECT given three positive integers $x, y$ and $z$ ... always true irrespective of the value of $x$ $P(x)$ being true means that $x$ has exactly two factors other than $1$ and $x$
admin asked in Mathematical Logic Apr 18, 2020
by admin
585 points
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0 answers 25 views
GATE2013-47 Video Solution
Which one of the following is NOT logically equivalent to $¬∃x(∀ y (α)∧∀z(β ))$ ? $∀ x(∃ z(¬β )→∀ y(α))$ $∀x(∀ z(β )→∃ y(¬α))$ $∀x(∀ y(α)→∃z(¬β ))$ $∀x(∃ y(¬α)→∃z(¬β ))$
admin asked in Mathematical Logic Apr 18, 2020
by admin
585 points
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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
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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
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GATE2013-27 Video Solution
What is the logical translation of the following statement? "None of my friends are perfect." $∃x(F (x)∧ ¬P(x))$ $∃ x(¬ F (x)∧ P(x))$ $ ∃x(¬F (x)∧¬P(x))$ $ ¬∃ x(F (x)∧ P(x))$
admin asked in Mathematical Logic Apr 18, 2020
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585 points
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