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Recent questions and answers in Mathematical Logic
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pigeon hole principle
Each of 15 red balls and 15 green balls is marked with an integer between 1 and 100 inclusive; no integer appears on more than one ball. The value of a pair of balls is the sum of the numbers on the balls. Show there are at least two pairs, consisting of one red and one green ball, with the same value. Show that this is not true if there are 13 balls of each color.
asked
22 hours
ago
in
Mathematical Logic
by
divi2719
(
7
points)

7
views
0
votes
0
answers
PROBABILTY AND DISTRIBUTIONS
A elevator manufacturing company believes that 'X' is the amount of that can elevator withstand without any damage with is mean 100 and standard deviation 10. This elevator is used to lift the company staff persons with mean 5 and standard deviation 0.5. How many staff person would have to be in the elevator for the probability of No damage exceeds to 0.85.
asked
Jun 30
in
Mathematical Logic
by
Stanfordboi
(
6
points)

8
views
discrete_maths
probability
poissondistribution
binomialdistribution
0
votes
0
answers
Combinatorics Simple doubt
What is the difference between flipping a pair of Distinct dices and flipping a pair of Identical Dices ??
asked
Jun 18
in
Mathematical Logic
by
BHASHKAR
(
47
points)

10
views
discrete_maths
permutation&combination
#discrete_maths
#combinatory
0
votes
0
answers
Kenneth Rosen 7th edition chapter 1.5 Exercise 12
Let I(x)be the statement x has an Internet connection and C(x,y) be the statement x and y have chatted over the Internet, where the domain for the variables x and y consists of all students in your class. Use quantiﬁers ... to ask what will be the answer if statement means there are exactly two students who have not chatted with each other .
asked
May 27
in
Mathematical Logic
by
ayush.5
(
13
points)

8
views
kennethrosen
#discrete_maths
0
votes
0
answers
If A is a square matrix of order n, then number of elementary product of A.
asked
May 14
in
Mathematical Logic
by
iamHarin
(
8
points)

11
views
0
votes
0
answers
Tree self doubt
A certain tree of order n has only vertices of degree 1 and degree 3. How many degree3 vertices does the tree have? (A). (B). (C). (D).
asked
May 8
in
Mathematical Logic
by
Abhipsa
(
27
points)

15
views
+1
vote
0
answers
Havell Hakimi Algorithm  Graph Theory
The Havell Hakimi Algorithm Requires the sorting of the degree sequence and later marking and subtracting according to that order. Does this means that the vertex with the highest degree will always have an edge with the vertex with the second ... I have noticed that without sorting the algorithm doesn't give correct output so I think it is a necessary step)
asked
May 5
in
Mathematical Logic
by
nilotpola
(
7
points)

32
views
discrete_maths
graphtheory
graph
0
votes
0
answers
Discrete Mathematics  Set Theory
Can we say that total order relations are same as algebraic structure as in both the cases, we are enclosing the structures under some operation?
asked
May 4
in
Mathematical Logic
by
roh
(
17
points)

3
views
discrete_maths
#group
#discrete_maths
#relations
#totallyorderedrelations
0
votes
0
answers
Cse zeal modules
How many subsets A of {1,2 3,....,10} have the property that no two elements of A sum to 11
asked
Apr 25
in
Mathematical Logic
by
Syywyeye
(
9
points)

19
views
0
votes
0
answers
This question is from gate cse zeal acadmey module
asked
Apr 25
in
Mathematical Logic
by
Syywyeye
(
9
points)

15
views
0
votes
0
answers
GATE201828 Video Solution
Consider the firstorder 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 $7$
asked
Apr 19
in
Mathematical Logic
by
admin
(
3.6k
points)

8
views
gate2018
mathematicallogic
normal
firstorderlogic
videosolution
0
votes
0
answers
GATE2016201 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 ___________.
asked
Apr 19
in
Mathematical Logic
by
admin
(
3.6k
points)

3
views
gate20162
mathematicallogic
normal
numericalanswers
propositionallogic
videosolution
0
votes
0
answers
GATE2015255 Video Solution
Which one of the following wellformed formulae is a tautology? $\forall x \, \exists y \, R(x,y) \, \leftrightarrow \, \exists y \, \forall x \, R(x, y)$ ... $\forall x \, \forall y \, P(x,y) \, \rightarrow \, \forall x \, \forall y \, P(y, x)$
asked
Apr 19
in
Mathematical Logic
by
admin
(
3.6k
points)

2
views
gate20152
mathematicallogic
normal
firstorderlogic
videosolution
0
votes
0
answers
GATE201935 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
asked
Apr 19
in
Mathematical Logic
by
admin
(
3.6k
points)

2
views
gate2019
engineeringmathematics
discretemathematics
mathematicallogic
firstorderlogic
videosolution
0
votes
0
answers
GATE2016227 Video Solution
Which one of the following wellformed formulae in predicate calculus is NOT valid ? $(\forall _{x} p(x) \implies \forall _{x} q(x)) \implies (\exists _{x} \neg p(x) \vee \forall _{x} q(x))$ ... $\forall x (p(x) \vee q(x)) \implies (\forall x p(x) \vee \forall x q(x))$
asked
Apr 19
in
Mathematical Logic
by
admin
(
3.6k
points)

2
views
gate20162
mathematicallogic
firstorderlogic
normal
videosolution
0
votes
0
answers
GATE2017102 Video Solution
Consider the firstorder logic sentence $F:\forall x(\exists yR(x,y))$. Assuming nonempty 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
asked
Apr 19
in
Mathematical Logic
by
admin
(
3.6k
points)

3
views
gate20171
mathematicallogic
firstorderlogic
videosolution
0
votes
0
answers
GATE200332 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) $((∀x)[α] ⇒ (∀x)[β]) ⇒ (∀x)[α ⇒ β]$ $(∀x)[α] ⇒ (∃x)[α ∧ β]$ $((∀x)[α ∨ β] ⇒ (∃x)[α]) ⇒ (∀x)[α]$ $(∀x)[α ⇒ β] ⇒ (((∀x)[α]) ⇒ (∀x)[β])$
asked
Apr 19
in
Mathematical Logic
by
admin
(
3.6k
points)

2
views
gate2003
mathematicallogic
firstorderlogic
normal
videosolution
0
votes
0
answers
GATE2015324 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
asked
Apr 19
in
Mathematical Logic
by
admin
(
3.6k
points)

2
views
gate20153
mathematicallogic
difficult
logicalreasoning
videosolution
0
votes
0
answers
GATE199292,xv Video Solution
Which of the following predicate calculus statements is/are valid? $(\forall (x)) P(x) \vee (\forall(x))Q(x) \implies (\forall (x)) (P(x) \vee Q(x))$ $(\exists (x)) P(x) \wedge (\exists (x))Q(x) \implies (\exists (x)) (P(x) \wedge Q(x))$ ... $(\exists (x)) (P(x) \vee Q(x)) \implies \sim (\forall (x)) P(x) \vee (\exists (x)) Q(x)$
asked
Apr 19
in
Mathematical Logic
by
admin
(
3.6k
points)

3
views
gate1992
mathematicallogic
normal
firstorderlogic
videosolution
0
votes
0
answers
GATE200423, ISRO200732 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 $y$ ... $(\exists x) (\text{boy}(x) \land (\forall y) (\text{girl}(y) \rightarrow \text{taller}(x, y)))$
asked
Apr 19
in
Mathematical Logic
by
admin
(
3.6k
points)

8
views
gate2004
mathematicallogic
easy
isro2007
firstorderlogic
videosolution
0
votes
0
answers
GATE201611 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 ____________.
asked
Apr 19
in
Mathematical Logic
by
admin
(
3.6k
points)

2
views
gate20161
mathematicallogic
normal
numericalanswers
propositionallogic
videosolution
0
votes
0
answers
GATE201030 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
asked
Apr 19
in
Mathematical Logic
by
admin
(
3.6k
points)

3
views
gate2010
mathematicallogic
easy
firstorderlogic
videosolution
0
votes
0
answers
GATE20021.8 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) $(X\land \neg Z) \rightarrow Y$ $(X \land Y) \rightarrow \neg Z$ $X \rightarrow(Y\land \neg Z)$ $(X \rightarrow Y)\land \neg Z$
asked
Apr 19
in
Mathematical Logic
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admin
(
3.6k
points)

1
view
gate2002
mathematicallogic
normal
propositionallogic
videosolution
0
votes
0
answers
GATE200333 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 \(\alpha\)
asked
Apr 19
in
Mathematical Logic
by
admin
(
3.6k
points)

2
views
gate2003
mathematicallogic
difficult
firstorderlogic
videosolution
0
votes
0
answers
GATE2005IT36 Video Solution
Let $P(x)$ and $Q(x)$ ...
asked
Apr 19
in
Mathematical Logic
by
admin
(
3.6k
points)

2
views
gate2005it
mathematicallogic
firstorderlogic
normal
videosolution
0
votes
0
answers
GATE2008IT21 Video Solution
Which of the following first order formulae is logically valid? Here $\alpha(x)$ is a first order formula with $x$ as a free variable, and $\beta$ ... $[(\forall x, \alpha(x)) \rightarrow \beta] \rightarrow [\forall x, \alpha(x) \rightarrow \beta]$
asked
Apr 19
in
Mathematical Logic
by
admin
(
3.6k
points)

3
views
gate2008it
firstorderlogic
normal
videosolution
0
votes
0
answers
GATE2006IT21 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
asked
Apr 19
in
Mathematical Logic
by
admin
(
3.6k
points)

2
views
gate2006it
mathematicallogic
normal
firstorderlogic
videosolution
0
votes
0
answers
GATE200830 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 $\text{equivalent}$ ...
asked
Apr 19
in
Mathematical Logic
by
admin
(
3.6k
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2
views
gate2008
easy
mathematicallogic
firstorderlogic
videosolution
0
votes
0
answers
GATE2017211 Video Solution
Let $p, q, r$ ... $(\neg p \wedge r) \vee (r \rightarrow (p \wedge q))$
asked
Apr 19
in
Mathematical Logic
by
admin
(
3.6k
points)

2
views
gate20172
mathematicallogic
propositionallogic
videosolution
0
votes
0
answers
GATE201130 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 $x$
asked
Apr 19
in
Mathematical Logic
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admin
(
3.6k
points)

1
view
gate2011
mathematicallogic
normal
firstorderlogic
videosolution
0
votes
0
answers
GATE201347 Video Solution
Which one of the following is NOT logically equivalent to $¬∃x(∀ y (α)∧∀z(β ))$ ? $∀ x(∃ z(¬β )→∀ y(α))$ $∀x(∀ z(β )→∃ y(¬α))$ $∀x(∀ y(α)→∃z(¬β ))$ $∀x(∃ y(¬α)→∃z(¬β ))$
asked
Apr 19
in
Mathematical Logic
by
admin
(
3.6k
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2
views
mathematicallogic
normal
markstoall
gate2013
firstorderlogic
videosolution
0
votes
0
answers
GATE2014153 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) $
asked
Apr 19
in
Mathematical Logic
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admin
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3.6k
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1
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gate20141
mathematicallogic
normal
propositionallogic
videosolution
0
votes
0
answers
GATE19981.5 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
asked
Apr 19
in
Mathematical Logic
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admin
(
3.6k
points)

1
view
gate1998
mathematicallogic
easy
propositionallogic
videosolution
0
votes
0
answers
GATE201327 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))$
asked
Apr 19
in
Mathematical Logic
by
admin
(
3.6k
points)

2
views
gate2013
mathematicallogic
easy
firstorderlogic
videosolution
0
votes
0
answers
GATE200372 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
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Apr 19
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Mathematical Logic
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admin
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3.6k
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1
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gate2003
mathematicallogic
normal
propositionallogic
videosolution
0
votes
0
answers
GATE2017129 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
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Apr 19
in
Mathematical Logic
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admin
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1
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gate20171
mathematicallogic
propositionallogic
videosolution
0
votes
0
answers
GATE200541 Video Solution
What is the first order predicate calculus statement equivalent to the following? "Every teacher is liked by some student" $∀(x)\left[\text{teacher}\left(x\right) → ∃(y) \left[\text{student}\left(y\right) → \text{likes}\left(y,x\right)\right]\right]$ ...
asked
Apr 19
in
Mathematical Logic
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admin
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3.6k
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3
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gate2005
mathematicallogic
easy
firstorderlogic
videosolution
0
votes
0
answers
GATE200722 Video Solution
$\def\graph{\text{ Graph}} \def\connected{\text{ Connected}}$ Let $\graph(x)$ be a predicate which denotes that $x$ is a graph. Let $\connected(x)$ be a predicate which denotes that $x$ is connected. Which of the following first order logic sentences DOES NOT ... $\forall x \, \Bigl ( \graph(x) \implies \lnot \connected(x) \Bigr )$
asked
Apr 19
in
Mathematical Logic
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admin
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3.6k
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2
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gate2007
mathematicallogic
easy
firstorderlogic
videosolution
0
votes
0
answers
GATE2017101 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
asked
Apr 19
in
Mathematical Logic
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admin
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2
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gate20171
mathematicallogic
propositionallogic
easy
videosolution
0
votes
0
answers
GATE201431 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.
asked
Apr 19
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Mathematical Logic
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admin
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3.6k
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2
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gate20143
mathematicallogic
easy
propositionallogic
videosolution
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