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Recent questions tagged mathematical-logic
0
votes
0
answers
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
views
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
views
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
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
19
views
kenneth-rosen
discrete-mathematics
combinatory
mathematical-logic
propositional-logic
0
votes
0
answers
42
views
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
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
44
views
discrete-mathematics
kenneth-rosen
combinatory
mathematical-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
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
47
views
discrete-mathematics
kenneth-rosen
propositional-logic
combinatory
mathematical-logic
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
44
views
discrete-mathematics
kenneth-rosen
combinatory
mathematical-logic
propositional-logic
0
votes
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
18
views
general-aptitude
mathematical-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
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
35
views
digital-logic
boolean-algebra
mathematical-logic
0
votes
1
answer
299
views
Trapeziums : Mathematics
An equilateral triangle, with side of length 3n for some natural number n, is made of smaller equilateral triangles. See the figure below for the case n=2. A bucket-shaped trapezium shown in the right of the below figure is made from three equilateral triangles. Prove that it is possible to cover the remaining triangles with non-overlapping trapeziums.
sumitsehgal
asked
in
Study Resources
May 8, 2020
by
sumitsehgal
5
points
299
views
mathematical-logic
0
votes
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
33
views
gate2018
mathematical-logic
normal
first-order-logic
video-solution
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
17
views
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
17
views
gate2015-2
mathematical-logic
normal
first-order-logic
video-solution
0
votes
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
28
views
gate2019
engineering-mathematics
discrete-mathematics
mathematical-logic
first-order-logic
video-solution
0
votes
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
22
views
gate2016-2
mathematical-logic
first-order-logic
normal
video-solution
0
votes
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
29
views
gate2017-1
mathematical-logic
first-order-logic
video-solution
1
vote
0
answers
22
views
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
585
points
22
views
gate2003
mathematical-logic
first-order-logic
normal
video-solution
0
votes
0
answers
21
views
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
21
views
gate2015-3
mathematical-logic
difficult
logical-reasoning
video-solution
0
votes
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
26
views
gate1992
mathematical-logic
normal
first-order-logic
video-solution
0
votes
0
answers
38
views
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
38
views
gate2004
mathematical-logic
easy
isro2007
first-order-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
22
views
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
22
views
gate2010
mathematical-logic
easy
first-order-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
23
views
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
585
points
23
views
gate2003
mathematical-logic
difficult
first-order-logic
video-solution
0
votes
0
answers
21
views
GATE2005-IT-36 Video Solution
Let $P(x)$ and $Q(x)$ ...
admin
asked
in
Mathematical Logic
Apr 18, 2020
by
admin
585
points
21
views
gate2005-it
mathematical-logic
first-order-logic
normal
video-solution
0
votes
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
by
admin
585
points
11
views
gate2006-it
mathematical-logic
normal
first-order-logic
video-solution
0
votes
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
30
views
gate2008
easy
mathematical-logic
first-order-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
36
views
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
36
views
gate2011
mathematical-logic
normal
first-order-logic
video-solution
0
votes
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
25
views
mathematical-logic
normal
marks-to-all
gate2013
first-order-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
24
views
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
by
admin
585
points
24
views
gate2013
mathematical-logic
easy
first-order-logic
video-solution
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