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Recent questions and answers in Mathematical Logic
+2
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1
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find close form of generating function discrete mathematics kenneth rosen
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2 days
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Mathematical Logic
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kennethrosen
discretemathematics
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2
Rank of a matrix
Let A be a 4×3 real matrix with rank 2. Let B be transpose matrix of A. Which one of the following statement is TRUE? (a) Rank of BA is less than 2. (b) Rank of BA is equal to 2. (c) Rank of BA is greater than 2. (d) Rank of BA can be any number between 1 and 3.
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2 days
ago
in
Mathematical Logic
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Shubhgupta
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rankofmatrix
engineeringmathematics
matrix
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3
UGCNETNov2017III70
Consider a Takagi  Sugeno  Kang (TSK) Model consisting of rules of the form : If x1 is Ai1 and ... and xr is Air THEN y =fi (x1, x2, ..., xr) = bi0+bi1 x1+.....+birxr assume, $\alpha$i is the matching degree of rule i, then the total output of the model is given by : (1) y ... 1}^{L}$ fi (x1,x2,....., xr)/$\sum_{i=1}^{L}\alpha$i (4) y = maxi [$\alpha$i fi (x1,x2,....., xr)]
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3 days
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Mathematical Logic
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Roma_nagpal
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115
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14
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0
votes
0
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4
This question is from graph theory
What is the total number of vertices in a tree if there are 3n vertices of degree 2 and 2n vertices of degree n?
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4 days
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in
Mathematical Logic
by
Pratyush
(
7
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24
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+33
votes
7
answers
5
GATE2015324
In a room there are only two types of people, namely Type 1 and Type 2. Type 1 people always tell the truth and Type 2 people always lie. You give a fair coin to a person in that room, without knowing which type he is from and tell him to toss it and hide the ... The result is tail If the person is of Type 2, then the result is tail If the person is of Type 1, then the result is tail
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Mathematical Logic
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Ayush Upadhyaya
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3.2k
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gate20153
mathematicallogic
difficult
logicalreasoning
+22
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5
answers
6
GATE2008IT21
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 $\beta$ is a first order formula with no free variable. $[\beta \rightarrow (\exists x, \alpha(x))] \rightarrow [\forall x, ... ) \rightarrow \beta]$ $[(\forall x, \alpha(x)) \rightarrow \beta] \rightarrow [\forall x, \alpha(x) \rightarrow \beta]$
answered
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Mathematical Logic
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Ayush Upadhyaya
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2.4k
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gate2008it
firstorderlogic
normal
+26
votes
6
answers
7
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
answered
6 days
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Mathematical Logic
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Ayush Upadhyaya
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8.8k
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3.5k
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gate20171
mathematicallogic
firstorderlogic
0
votes
2
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8
self doubt
What is the English of both statement ∀x((x!=0)→∃y(xy=100)) ∀x∃y((x!=0)→(xy=100))
answered
Jun 16
in
Mathematical Logic
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Deepakk Poonia (Dee)
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13.2k
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32
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+2
votes
3
answers
9
UGCNETDec2014III57
The resolvent of the set of clauses $(A \vee B, \sim A \vee D, C \vee \sim B)$ is $A \vee​ B$ $C \vee​ D$ $A \vee​ C$ $A \vee​ D$
answered
Jun 16
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Mathematical Logic
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Prasanjeet Ghosh
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571
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ugcnetdec2014iii
mathematicallogic
+2
votes
3
answers
10
UGCNETDec2014III55
Equivalent logical expression for the Well Formed Formula $(WFF)$, $\sim(\forall x) F\left[x\right]$ is $\forall x (\sim F\left[x\right])$ $\sim (\exists x) F\left[x\right]$ $\exists x (\sim F\left[x\right])​$ $\forall x F\left[x\right]$
answered
Jun 16
in
Mathematical Logic
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Prasanjeet Ghosh
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431
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ugcnetdec2014iii
mathematicallogic
+2
votes
1
answer
11
Random_Doubt
if it is given > "Every satisfiable propositional formula is not tautology" then what will it corresponds to? i am writing its hindi, which among below two are correct? "har ek satisfiable formula tautology nahi hota hai" // it is indeed truth. "koi bhi satisfiable formula hua, to wo tautology nahii hoga" // this is false.
answered
Jun 16
in
Mathematical Logic
by
Vegeta
(
21
points)

33
views
discretemathematics
propositionallogic
0
votes
2
answers
12
IIT M video questions
P(x,y,z), xy=z, Universe is interger; write in logic form If xy=x for all y, then x =0. Thank you
answered
Jun 14
in
Mathematical Logic
by
Deepakk Poonia (Dee)
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13.2k
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51
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propositionallogic
firstorderlogic
logicalreasoning
0
votes
1
answer
13
self doubt
dog(x) = x is a dog Int (x) = x is intelligent write in logic form No dogs are intelligent.
answered
Jun 14
in
Mathematical Logic
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Deepakk Poonia (Dee)
Boss
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13.2k
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31
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propositionallogic
firstorderlogic
logicalreasoning
0
votes
0
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14
generating funtion
1/1−2x2 provide close formula for the sequences it determines
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Jun 14
in
Mathematical Logic
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sunil sarode
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1.1k
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14
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generatingfunctions
kennethrosen
discretemathematics
0
votes
0
answers
15
discrete maths
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? (A) Only L is TRUE. (B) Only M is TRUE. (C) Only N is TRUE. (D) L, M and N are TRUE
[closed]
asked
Jun 13
in
Mathematical Logic
by
Preety singhal
(
15
points)

18
views
+1
vote
1
answer
16
Gateoverflow pdf
answered
Jun 13
in
Mathematical Logic
by
Aarzoo Chourasia
(
11
points)

270
views
0
votes
0
answers
17
LogicKenneth Rosen (Ex1.411f)
Let S(x) be the predicate that "x is a student", F(x) be the predicate "x is a faculty member", and A(x,y) the predicate "x has asked y a question", where the domain consists of all people associated with your school. ... A(x,y) ) ) Doubt 2: What is the difference between my answer and rosen's answer.Which one is correct. Please help.
[closed]
asked
Jun 12
in
Mathematical Logic
by
Ayush Upadhyaya
Loyal
(
8.8k
points)

36
views
discretemathematics
propositionallogic
0
votes
0
answers
18
ISI 2014 MMA 9
asked
Jun 12
in
Mathematical Logic
by
Sammohan Ganguly
(
417
points)

21
views
userisi2014
usermod
engineeringmathematics
0
votes
0
answers
19
ISI 2014 MMA  3
asked
Jun 12
in
Mathematical Logic
by
Sammohan Ganguly
(
417
points)

23
views
userisi2014
usermod
engineeringmathematics
0
votes
2
answers
20
Sheldon ross Conditional probability
answered
Jun 12
in
Mathematical Logic
by
Shaik Masthan
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(
2.5k
points)

66
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sheldonross
probability
0
votes
1
answer
21
doubt in propositional logic
can someone explain NULL QUANTIFICATION in depth??
answered
Jun 11
in
Mathematical Logic
by
Deepakk Poonia (Dee)
Boss
(
13.2k
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72
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+1
vote
1
answer
22
Propositional Equivalences
Which of the following are true : 1. $\forall x (P(x) \Leftrightarrow Q(x) ) \rightarrow (\forall x P(x) \Leftrightarrow \forall x Q(x))$ 2. $\forall x (P(x) \Leftrightarrow Q(x) ) \leftarrow (\forall x P(x) \Leftrightarrow \forall x Q(x))$ 3. $\ ... exists x Q(x))$ 6. $\exists x (P(x) \Leftrightarrow Q(x) ) \Leftrightarrow (\exists x P(x) \Leftrightarrow \exists x Q(x))$
answered
Jun 11
in
Mathematical Logic
by
Deepakk Poonia (Dee)
Boss
(
13.2k
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65
views
0
votes
0
answers
23
LogicKenneth Rosen(Ex1.45e)
Let W(x,y) mean that student x has visited website y, where the domain for x consists of all students in your school and domain for y consists of all websites. Express below statement in the english sentence. ∃x∃y∀z ( (x$\neq$y) ^ ( ... two persons who have visited exactly the same set of websites." And this means exactly two. Which one is correct interpretation?
asked
Jun 10
in
Mathematical Logic
by
Ayush Upadhyaya
Loyal
(
8.8k
points)

27
views
discretemathematics
kennethrosen
propositionallogic
0
votes
0
answers
24
LogicKenneth Rosen(Ex1.357)
Let P(x)x is a baby Q(x) x is logical R(x)x is able to manage a crocodile S(x)x is despised. Suppose that the domain consists of all people.Express each of the these statements using quantifiers (a)Babies are illogical (b)Nobody is despised who can manage a ... x)) (c)∀x($\sim Q(x)\rightarrow S(x)$ ) (d)∀x($P(x)\rightarrow \sim R(x)$) Please verify my answers.
[closed]
asked
Jun 10
in
Mathematical Logic
by
Ayush Upadhyaya
Loyal
(
8.8k
points)

26
views
discretemathematics
kennethrosen
propositionallogic
0
votes
0
answers
25
SelfDoubtLogic
What is the negation of ∃x(x2=2) I think it is ∀x(x2$\neq$2)
asked
Jun 9
in
Mathematical Logic
by
Ayush Upadhyaya
Loyal
(
8.8k
points)

42
views
discretemathematics
mathematicallogic
0
votes
1
answer
26
Distinguishable objects and indistinguishable boxes
answered
Jun 8
in
Mathematical Logic
by
Deepakk Poonia (Dee)
Boss
(
13.2k
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75
views
permutationsandcombinations
0
votes
1
answer
27
Null Qunatification Rule
What is the meaning of NULL Quantification Rule in Predicate Calculus ?
answered
Jun 8
in
Mathematical Logic
by
Deepakk Poonia (Dee)
Boss
(
13.2k
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78
views
discretemathematics
propositionallogic
0
votes
1
answer
28
Gate Previous year
Consider the following formula and its two interpretations $I1$ and $I2$. $α:(∀x)[Px⇔(∀y)[Qxy⇔¬Qyy]]⇒(∀x)[¬Px]$ $I1 :$ Domain: the set of natural numbers $Px =$ $\text{'x is a prime number'}$ $Qxy =\text{ 'y divides x'}$ $I2 :$ same as ... for all $x$ quantifier is going to pick every composite number value from the set and the domain of $Y:\text{{set of all natural numbers}}$
answered
Jun 7
in
Mathematical Logic
by
muthu kumar
(
219
points)

46
views
engineeringmathematics
mathematicallogic
+3
votes
1
answer
29
predicate logic
Recall that a predicate logic statement is contingent if its truth value depends on the choice of the universe and on the interpretations of the predicate symbol S and the constant symbol b involved. Consider the following predicate logic statements in which b, x ...  Contingent  Always false (C) Always true  Contingent  Contingent (D) Contingent  Always true  Always false
answered
Jun 6
in
Mathematical Logic
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Deepakk Poonia (Dee)
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13.2k
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72
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mathematicallogic
propositionallogic
firstorderlogic
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+1
vote
1
answer
30
Kennth Rosen,ch:1,Ex:1.3,Qn:51
Find a compound proposition logically equivalent to $p \rightarrow q$ using only the logical operator $\downarrow$?
answered
Jun 5
in
Mathematical Logic
by
Deepakk Poonia (Dee)
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13.2k
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39
views
kennethrosen
settheory&algebra
propositionallogic
mathematicallogic
descriptive
0
votes
2
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31
Express the statement in logical expression
answered
Jun 5
in
Mathematical Logic
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Deepakk Poonia (Dee)
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301
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propositionallogic
+1
vote
1
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32
Kenneth Rosen Ch:1,Ex:1.5 Qn:52.
Express the quantification $∃!xP (x)$,using universal quantifications, existential quantifications, and logical operators.?
answered
Jun 5
in
Mathematical Logic
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Deepakk Poonia (Dee)
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69
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discretemathematics
engineeringmathematics
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33
Sheldon ross(9th ed.)chapter 2 example 5(g)
asked
Jun 4
in
Mathematical Logic
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Prateek Raghuvanshi
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23
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0
votes
0
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34
Kennth Rosen Ch:1,Ex:1.2, Qn:38.
Solve this famous logic puzzle, attributed to Albert Einstein, and known as the zebra puzzle.Five men with different nationalities and with different jobs live in consecutive houses on a street. These houses are painted different colors. The men ... , their pets, and their favorite drinks and use logical reasoning to determine the correct entries in the table.]?
asked
Jun 3
in
Mathematical Logic
by
siva140191
(
63
points)

51
views
kennethrosen
mathematicallogic
settheory&algebra
propositionallogic
descriptive
0
votes
2
answers
35
Number of ordered pairs
answered
Jun 1
in
Mathematical Logic
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Deepakk Poonia (Dee)
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13.2k
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46
views
0
votes
1
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36
Test series
How to do these type of questions?
answered
Jun 1
in
Mathematical Logic
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Deepakk Poonia (Dee)
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13.2k
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48
views
0
votes
1
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37
Made easy test
answered
May 31
in
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Deepakk Poonia (Dee)
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13.2k
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52
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0
votes
1
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38
Combinatorics
Among the integers $1,2,3,....,200$ if $101$ integers are chosen,then show that there are two among the chosen,such that one is divisible by the other.
answered
May 31
in
Mathematical Logic
by
Kushagra Chatterjee
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8.2k
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49
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engineeringmathematics
discretemathematics
permutationsandcombinations
pigeonholeprinciple
counting
0
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1
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39
Group Theory
Let G and G1 be two groups such that G1 is a homomorphic image of G. If G is a cyclic group then so is G1.
answered
May 31
in
Mathematical Logic
by
Kushagra Chatterjee
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8.2k
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19
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groups
0
votes
1
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40
Group theory
Let G and G1 be two groups such that G1 is a homomorphic image of G. Prove that if G is a commutative group,then so is G1.
answered
May 31
in
Mathematical Logic
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Kushagra Chatterjee
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8.2k
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15
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