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Propositional and first order logic.
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Random variable
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Mathematical Logic
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GATE Minimum Spanning Trees
Q1) Why is the path between a pair of vertices in a minimum Spanning tree of an undirected graph not the shortest( minimum weight) path?
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Mathematical Logic
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Shaik Masthan
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minimumspanningtrees
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Made_Easy
The minimum number of edges the graph G should have for the graph G to a 3connected and it given that G has 10 vertices ?
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Mathematical Logic
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srestha
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6
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4
GATE200722
$\def\graph{\text{ Graph}} \def\connected{\text{ Connected}}$ 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 represent the statement ... (x) \lor \connected(x) \Bigr )$ $\forall x \, \Bigl ( \graph(x) \implies \lnot \connected(x) \Bigr )$
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Mathematical Logic
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monika7537
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19
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gate2007
mathematicallogic
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firstorderlogic
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1
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5
Gate previous year question
A fair coin is tossed repeatedly until both head and tail appears atleast once. The average number of tosses
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Mathematical Logic
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sudoankit
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3
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6
GATE200332
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) $((∀x)[α] ⇒ (∀x)[β]) ⇒ (∀x)[α ⇒ β]$ $(∀x)[α] ⇒ (∃x)[α ∧ β]$ $((∀x)[α ∨ β] ⇒ (∃x)[α]) ⇒ (∀x)[α]$ $(∀x)[α ⇒ β] ⇒ (((∀x)[α]) ⇒ (∀x)[β])$
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Mathematical Logic
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dupchik
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9
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3.4k
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gate2003
mathematicallogic
firstorderlogic
normal
0
votes
1
answer
7
Propositional Logic
Ans. A
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Mathematical Logic
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87
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propositionallogic
mathematicallogic
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8
Mathematical Logic
prove $(¬A→¬B)∧(A→C)→(B→C)$
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9
Summations.
Plz solve in steps: $\sum_{i=0}^{k}$$n^{1/2^i}$
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10
Rosen 6.5 Exercise 19
Suppose that a large family has 14 children, including two sets of identical triplets, three sets of identical twins, and two individual children. How many ways are there to seat these children in a row of chairs if the identical triplets or twins ... objects when they are neighborhood or not. But the question had asked for similar objects sit side by side. Please clarify
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Shaik Masthan
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kennethrosen
permutationsandcombinations
+2
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1
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11
Number of ways ... distinguishable into distinguishable.
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Mathematical Logic
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Abhijit Sen 4
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257
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permutationsandcombinations
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1
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12
GATE2004IT3
Let $a(x, y), b(x, y,)$ and $c(x, y)$ be three statements with variables $x$ and $y$ chosen from some universe. Consider the following statement: $\qquad(\exists x)(\forall y)[(a(x, y) \wedge b(x, y)) \wedge \neg c(x, y)]$ Which one of the following is its equivalent? $(\forall x)(\exists ... b(x, y)) \to c(x, y)]$ $\neg (\forall x)(\exists y)[(a(x, y) \vee b(x, y)) \to c(x, y)]$
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4
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13
GATE200923
Which one of the following is the most appropriate logical formula to represent the statement? "Gold and silver ornaments are precious". The following notations are used: $G(x): x$ is a gold ornament $S(x): x$ is a silver ornament $P(x): x$ is precious $\forall x(P(x) \implies (G(x) \ ... $\exists x((G(x) \wedge S(x)) \implies P(x))$ $\forall x((G(x) \vee S(x)) \implies P(x))$
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Mathematical Logic
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JAY BHUTADA
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25
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gate2009
mathematicallogic
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firstorderlogic
+4
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14
CMI2015A01
Twin primes are pairs of numbers $p$ and $p+2$ such that both are primesfor instance, 5 and 7, 11 and 13, 41 and 43. The Twin Prime Conjecture says that there are infinitely many twin primes. Let $TwinPrime(n)$ be a predicate that is true if $n$ and $n+2$ are twin primes. ... ) $∃m. ∀n. n ≤ m$ implies TwinPrime(n) $∀m. ∃n. n ≤ m$ and TwinPrime(n) $∃m. ∀n.$ TwinPrime(n) implies $n ≤ m$
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Mathematical Logic
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2
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15
GATE199115,b
(b) Consider the following first order formula: $\left ( \matrix{ \forall x \exists y : R(x,y) \\[1em] \Large \land \\[1em] \forall x \forall y : \left ( R(x,y) \implies \lnot R(y,x) \right) \\[1em] \Large \land \\[1em] \forall x \forall y \forall ... \land \\[1em] \forall x: \lnot R(x,x) }\right )$ Does it have finite models? Is it satisfiable? If so, give a countable model for it.
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gate1991
firstorderlogic
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16
Techtud quiz
Twin primes are pairs of numbers pp and p+2p+2 such that both are primesfor instance, 5 and 7, 11 and 13, 41 and 43. The Twin Prime Conjecture says that there are infinitely many twin primes. Let TwinPrime(n)TwinPrime(n) be a predicate that is true if nn and n ... (n)) ∃m.∀n.n≤m∃m.∀n.n≤m implies TwinPrime(n) ∀m.∃n.n≤m∀m.∃n.n≤m and TwinPrime(n) ∃m.∀n.∃m.∀n. TwinPrime(n) implies n≤m
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firstorderlogic
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17
Probability
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291
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18
Probability
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+26
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6
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19
GATE2017102
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
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Mathematical Logic
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gate20171
mathematicallogic
firstorderlogic
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1
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20
Virtual GATE
Which of the following statements is TRUE about the propositional logic formula S:(p→q)∧(¬q∨r)∧(r→s)→¬(p→s) (A) S is a contradiction (B) S is satisfiable but not valid (C) S is valid (D) None of the above
answered
Sep 16
in
Mathematical Logic
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krbablu
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11
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testseries
virtualgate
discretemathematics
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0
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21
Time complexity of given code using "finite" geometric series
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Sep 15
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Mathematical Logic
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GateAspirant999
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0
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22
S is increasing function or not?
Consider the following statements. S1: f(x) = x5 + 3x  1 is an increasing function for all values of x. S2: f(x) = 1x3x9 is decreasing function for all values of x where x 0. Which of the above statements are TRUE. AS1 only BS2 only CBoth S1 and S2 DNeither S1 nor S2
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engineeringmathematics
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23
Syllabus:Numerical methods like newton method or bisection method part of syllabus of Gate?
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Sep 15
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Mathematical Logic
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gate
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1
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24
UGCNETJune2012III17
Let $Q(x,y)$ denote “x+y=0” and let there be two quantifications given as $\exists y \forall x Q(x,y)$ $\forall x \exists y Q(x,y)$ where $x$ and $y$ are real numbers. Then which of the following is valid? I is true and II is false I is false and II is true I is false and II is also false both I and II are true
edited
Sep 15
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Mathematical Logic
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Sanjay Sharma
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discretemathematics
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25
Maths: Limit question
Lim n>infinity (n*2^n)/e^n Detailed solution please?
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Sep 14
in
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chauhansunil20th
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209
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limits
calculus
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26
ace booklet
whats ans of this qn and please explain
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Sep 13
in
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Vegeta
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287
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acebooklet
engineeringmathematics
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0
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1
answer
27
Self doubt
What does ∃y∀xQ(x,y) mean where Q(x,y) denotes x+y=0 ?
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Sep 11
in
Mathematical Logic
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Abhinavg
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351
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discreetmaths
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0
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28
Gate EC 2005
asked
Sep 11
in
Mathematical Logic
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Shiv kumari
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9
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6
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0
votes
2
answers
29
PigeonHole Principal
A drawer contains a dozen of brown and dozen of black socks,all unmatched.A man takes socks out at random in the dark. How many socks must he take out to be sure that he has atleast two black socks ?
answered
Sep 11
in
Mathematical Logic
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Sumit Rana 1
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297
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permutationsandcombinations
counting
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30
asin^2x +blogcosx/x^4
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Sep 11
in
Mathematical Logic
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16
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0
votes
0
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31
Test Series
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Sep 9
in
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ben10
(
301
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22
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+3
votes
1
answer
32
UGCNETDec2012III19
Identify the following activation function: $\Phi (V) = Z +\frac{1}{1+ exp(x*V+Y)}$, Z, X, Y are parameters. Step function Ramp function Sigmoid function Gaussian function
comment edited
Sep 9
in
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anchitjindal07
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ugcnetdec2012iii
discretemathematics
functions
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2
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33
propositional logic
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Sep 9
in
Mathematical Logic
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vijju532
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0
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34
Maxima #minima
In first question stationary point is given pi/4 and 3pi/4 . But how 3pi/4 ??? Its not in the intervel ??
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Sep 9
in
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abhishekmehta4u
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9
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35
Logic
comment edited
Sep 8
in
Mathematical Logic
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Mk Utkarsh
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43
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0
votes
0
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36
Predicate logic gatebook test on logic Q4
[closed]
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Sep 8
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Shaik Masthan
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firstorderlogic
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0
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37
Predicate logic gatebook test on logic Q13
[closed]
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mathematicallogic
firstorderlogic
propositionallogic
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38
Predicate logic gatebook test on logic Q18
[closed]
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39
Logic
answered
Sep 8
in
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Mohit Kumar 6
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497
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124
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0
votes
1
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40
GATE 2018
What is the answer?
answered
Sep 8
in
Mathematical Logic
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Mohit Kumar 6
(
497
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715
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propositionallogic
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