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Recent questions and answers in Mathematical Logic
0
votes
1
answer
1
Maths
HOW MANY ways we can distribute 10 objects to 3 children so that every child gets atleast one object?
answered
3 days
ago
in
Mathematical Logic
by
Raghav Khajuria
Junior
(
807
points)

58
views
+33
votes
5
answers
2
GATE201130
Which one of the following options is CORRECT given three positive integers $x, y$ and $z$ ... is always true irrespective of the value of $x$ $P(x)$ being true means that $x$ has exactly two factors other than $1$ and $x$
answered
4 days
ago
in
Mathematical Logic
by
Rishiryanemo
(
29
points)

3.9k
views
gate2011
mathematicallogic
normal
firstorderlogic
+31
votes
8
answers
3
GATE2005IT36
Let $P(x)$ and $Q(x)$ ...
answered
Jan 16
in
Mathematical Logic
by
Madhab
Loyal
(
5.8k
points)

4.6k
views
gate2005it
mathematicallogic
firstorderlogic
normal
0
votes
1
answer
4
ugc net 2018 july79
answered
Jan 14
in
Mathematical Logic
by
mishrapankajs
(
11
points)

250
views
+2
votes
1
answer
5
ISRO202073
Given that $B(a)$ means “$a$ is a bear” $F(a)$ means “$a$ is a fish” and $E(a,b)$ means “$a $ eats $b$” Then what is the best meaning of $\forall x [F(x) \to \forall y(E(y,x)\rightarrow b(y))]$ Every fish is eaten by some bear Bears eat only fish Every bear eats fish Only bears eat fish
answered
Jan 13
in
Mathematical Logic
by
chirudeepnamini
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(
4.5k
points)

245
views
isro2020
discretemathematics
mathematicallogic
propositionallogic
normal
0
votes
1
answer
6
Kenneth Rosen Edition 7th Exercise 1.7 Question 7 (Page No. 91)
Use a direct proof to show that every odd integer is the difference of two squares.
answered
Jan 5
in
Mathematical Logic
by
vedantbonde19
(
29
points)

23
views
kennethrosen
discretemathematics
mathematicallogic
propositionallogic
0
votes
1
answer
7
Kenneth Rosen Edition 7th Exercise 1.7 Question 15 (Page No. 91)
Use a proof by contraposition to show that if $x+y≥2$,where $x$ and $y$ are real numbers, then $x≥1$ or $y≥1$.
answered
Jan 5
in
Mathematical Logic
by
vedantbonde19
(
29
points)

13
views
kennethrosen
discretemathematics
mathematicallogic
propositionallogic
+1
vote
1
answer
8
Kenneth Rosen Edition 7th Exercise 1.7 Question 11 (Page No. 91)
Prove or disprove that the product of two irrational numbers is irrational.
answered
Jan 5
in
Mathematical Logic
by
vedantbonde19
(
29
points)

22
views
kennethrosen
discretemathematics
mathematicallogic
propositionallogic
+1
vote
1
answer
9
Kenneth Rosen Edition 7th Exercise 1.7 Question 10 (Page No. 91)
Use a direct proof to show that the product of two rational numbers is rational.
answered
Jan 5
in
Mathematical Logic
by
vedantbonde19
(
29
points)

9
views
kennethrosen
discretemathematics
mathematicallogic
propositionallogic
+1
vote
1
answer
10
ME FLT
Consider the following statements with respect to POSETs. I. Every non empty, finite POSET has at least one maximal and at least one minimal element. II. Every POSET has at most one greatest element and at most one least element. Which of the above statement(s) is/are true?
answered
Jan 1
in
Mathematical Logic
by
Veenit
Active
(
1.6k
points)

44
views
discretemathematics
+24
votes
4
answers
11
GATE19981.5
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
answered
Dec 31, 2019
in
Mathematical Logic
by
JashanArora
Loyal
(
6.9k
points)

3.5k
views
gate1998
mathematicallogic
easy
propositionallogic
0
votes
3
answers
12
Express the statement in logical expression
Express the statement "Everyone has exactly one best friend" as a logical expression involving predicates,quantifiers with a domain consisting of all people,and logical connectives without using uniqueness quantifier. I am confused pleased explain it
answered
Dec 28, 2019
in
Mathematical Logic
by
rohithk
(
11
points)

473
views
propositionallogic
0
votes
2
answers
13
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?
answered
Dec 17, 2019
in
Mathematical Logic
by
smsubham
Boss
(
11.8k
points)

190
views
minimumspanningtrees
spanningtree
graphtheory
graphalgorithms
algorithms
+2
votes
1
answer
14
Hamiltonian Graph
A complement of a cyclic graph on 5 vertices , has an Hamiltonian circuit . (True/False)
answered
Dec 11, 2019
in
Mathematical Logic
by
Anup dogrial
(
339
points)

284
views
graphtheory
discretemathematics
+26
votes
3
answers
15
GATE199115,b
Consider the following first order formula: ... Does it have finite models? Is it satisfiable? If so, give a countable model for it.
answered
Dec 11, 2019
in
Mathematical Logic
by
pritishc
Active
(
2.2k
points)

1.9k
views
gate1991
firstorderlogic
descriptive
+13
votes
8
answers
16
GATE201935
Consider the first order predicate formula $\varphi$: $\forall x [ ( \forall z \: z \mid x \Rightarrow (( z=x) \vee (z=1))) \rightarrow \exists w ( w > x) \wedge (\forall z \: z \mid w \Rightarrow ((w=z) \vee (z=1)))]$ Here $a \mid b$ ... Set 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
answered
Dec 10, 2019
in
Mathematical Logic
by
Deepakk Poonia (Dee)
Boss
(
27.6k
points)

6k
views
gate2019
engineeringmathematics
discretemathematics
mathematicallogic
firstorderlogic
+37
votes
7
answers
17
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 $\beta$ ... $[(\forall x, \alpha(x)) \rightarrow \beta] \rightarrow [\forall x, \alpha(x) \rightarrow \beta]$
answered
Nov 26, 2019
in
Mathematical Logic
by
JashanArora
Loyal
(
6.9k
points)

4.7k
views
gate2008it
firstorderlogic
normal
+33
votes
7
answers
18
GATE20021.8
"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) $(X\land \neg Z) \rightarrow Y$ $(X \land Y) \rightarrow \neg Z$ $X \rightarrow(Y\land \neg Z)$ $(X \rightarrow Y)\land \neg Z$
answered
Nov 11, 2019
in
Mathematical Logic
by
Navneet Singh Tomar
Junior
(
783
points)

4.8k
views
gate2002
mathematicallogic
normal
propositionallogic
0
votes
2
answers
19
solution of rosen
can anyone has the soft copy of kenneth h rosen solutions?
answered
Nov 11, 2019
in
Mathematical Logic
by
Ram Swaroop
Loyal
(
5.4k
points)

439
views
+2
votes
3
answers
20
Rosen chapter 5.5 question 50
How many ways are there to distribute 5 distinguishable objects into three indistinguishable boxes?
answered
Nov 9, 2019
in
Mathematical Logic
by
SaurabhKatkar
(
241
points)

245
views
+10
votes
4
answers
21
GATE19893v
Answer the following: Which of the following wellformed formulas are equivalent? $P \rightarrow Q$ $\neg Q \rightarrow \neg P$ $\neg P \vee Q$ $\neg Q \rightarrow P$
answered
Oct 8, 2019
in
Mathematical Logic
by
vupadhayayx86
Active
(
1.7k
points)

676
views
gate1989
normal
mathematicallogic
propositionallogic
+25
votes
5
answers
22
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 $P(x): x$ ... $\exists x((G(x) \wedge S(x)) \implies P(x))$ $\forall x((G(x) \vee S(x)) \implies P(x))$
answered
Sep 17, 2019
in
Mathematical Logic
by
manikantsharma
(
429
points)

2k
views
gate2009
mathematicallogic
easy
firstorderlogic
0
votes
0
answers
23
CMI2019B5
In the land of Twitter, there are two kinds of people: knights (also called outragers), who always tell the truth, and knaves (also called trolls), who always lie. It so happened that a person with handle @anand tweeted something offensive. It was not known whether @anand was ... $ 1$ : @anand once claimed that I was a knave. Chitra : Are you by any chance @anand? Suspect $1$ : Yes.
asked
Sep 13, 2019
in
Mathematical Logic
by
gatecse
Boss
(
17.5k
points)

52
views
cmi2019
mathematicallogic
logicalreasoning
0
votes
1
answer
24
Kenneth Rosen Edition 7th Exercise 1.6 Question 30 (Page No. 80)
Use resolution to show the hypotheses “Allen is a bad boy or Hillary is a good girl” and “Allen is a good boy or David is happy” imply the conclusion “Hillary is a good girl or David is happy.”
answered
Sep 7, 2019
in
Mathematical Logic
by
tejamach
(
11
points)

25
views
kennethrosen
discretemathematics
mathematicallogic
propositionallogic
+1
vote
1
answer
25
How do I prepare Engineering Mathematics for Gate CS?
Good Morning, I want to start Engineering Mathematics and need help from you to know where to start and what would be the best sequence to complete the whole subject?
answered
Sep 4, 2019
in
Mathematical Logic
by
Akashniranjan
(
17
points)

670
views
preparation
general
+1
vote
2
answers
26
UGCNETJune2013II40
The truth value of the statements: $\exists ! xP(x) \rightarrow \exists xP(x) \text{ and } \exists ! x \rceil P(x) \rightarrow \rceil \forall xP(x)$, (where the notation $\exists ! x P(x)$ denotes the proposition “There exists a unique $x$ such that $P(x)$ is true”) are: True and False False and True False and False True and True
answered
Aug 31, 2019
in
Mathematical Logic
by
GoalSet1
(
215
points)

589
views
ugcnetjune2013ii
+2
votes
2
answers
27
Find the number of into functions
answered
Aug 26, 2019
in
Mathematical Logic
by
Lakshman Patel RJIT
Veteran
(
59.3k
points)

1.4k
views
+1
vote
1
answer
28
Knights , Knaves , spy
answered
Aug 24, 2019
in
Mathematical Logic
by
Kushagra गुप्ता
Active
(
4.5k
points)

104
views
+30
votes
3
answers
29
GATE201431
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.
answered
Aug 16, 2019
in
Mathematical Logic
by
sohailkhan
(
75
points)

2.9k
views
gate20143
mathematicallogic
easy
propositionallogic
0
votes
1
answer
30
recurrence relation
Which recurrence relation satisfy the sequence: 2, 3, 4, . . ., for n ≥ 1. A ) T(N) = 2 T(N1)  T(N2) B)T(N) = T(N1) + T(N2) C)T(N) = N+1 D) None of these
answered
Aug 8, 2019
in
Mathematical Logic
by
Rohit Suryanarayan
(
17
points)

530
views
recurrence
+58
votes
4
answers
31
GATE200333
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: the set of ... , \(I_1\) does not Neither \(I_1\) nor \(I_2\) satisfies \(\alpha\) Both \(I_1\) and \(I_2\) satisfies \(\alpha\)
answered
Aug 6, 2019
in
Mathematical Logic
by
MRINMOY_HALDER
Active
(
4k
points)

4.8k
views
gate2003
mathematicallogic
difficult
firstorderlogic
0
votes
1
answer
32
Probability
Prabha is working in a software company. Her manager is running a dinner for those employees having atleast one son. If Prabha is invited to the dinner and everyone knows she has two children. What is the probability that they are both boys?
answered
Jul 20, 2019
in
Mathematical Logic
by
bankeshk
(
79
points)

64
views
probability
engineeringmathematics
conditionalprobability
+1
vote
1
answer
33
relation
A binary relation R on Z × Z is defined as follows: (a, b) R (c, d) iff a = c or b = d Consider the following propositions: 1. R is reflexive. 2. R is symmetric. 3. R is antisymmetric. Which one of the following statements is True? A Both 1 and 2 are true B 1 is true and 2 is false C 1 is false and 3 is true D Both 2 and 3 are true
answered
Jul 12, 2019
in
Mathematical Logic
by
mohan123
Active
(
1.7k
points)

83
views
+5
votes
2
answers
34
UGCNETJune2019II8
Match ListI with ListII: ... )  (iv); (b)  (i); (c)  (iii); (d)  (ii) (a)  (iv); (b)  (iii); (c)  (i); (d)  (ii)
answered
Jul 7, 2019
in
Mathematical Logic
by
Lakshmikanta
(
69
points)

218
views
ugcnetjune2019ii
propositionallogic
+4
votes
2
answers
35
UGCNETJune2019II6
Which of the following is principal conjunctive normal form for $[(p\vee q)\wedge\ \rceil p \rightarrow \rceil q ]$ ? $p\ \vee \rceil q$ $p \vee q $ $\rceil p \vee q$ $\rceil p\ \vee \rceil q$
answered
Jul 7, 2019
in
Mathematical Logic
by
Satbir
Boss
(
24.2k
points)

337
views
ugcnetjune2019ii
propositionallogic
0
votes
1
answer
36
MadeEasy Test Series: Probability
How to get the idea that we have to use Binomial distribution or Hypergeometric Distribution. I know that if the probability is not changing(i.e with replacement) then we go Binomial otherwise Hypergeometric. But in question, it is not indicating ... So is there any by default approach that we have to use Binomial if nothing is a mention about a replacement.
answered
Jun 13, 2019
in
Mathematical Logic
by
vizzard110
(
439
points)

51
views
madeeasytestseries
probability
binomialdistribution
+4
votes
1
answer
37
TIFR2017B6
Consider the First Order Logic (FOL) with equality and suitable function and relation symbols. Which of the following is FALSE? Partial orders cannot be axiomatized in FOL FOL has a complete proof system Natural numbers cannot be axiomatized in FOL Real numbers cannot be axiomatized in FOL Relational numbers cannot be axiomatized in FOL
answered
Jun 8, 2019
in
Mathematical Logic
by
Arjun
Veteran
(
431k
points)

249
views
tifr2017
firstorderlogic
normal
0
votes
1
answer
38
GATE198814i
Consider the following wellformed formula: $\exists x \forall y [ \neg \: \exists z [ p (y, z) \wedge p (z, y) ] \equiv p(x,y)]$ Express the above wellformed formula in clausal form.
answered
Jun 7, 2019
in
Mathematical Logic
by
Arjun
Veteran
(
431k
points)

183
views
gate1988
descriptive
firstorderlogic
clausalform
nongate
+1
vote
2
answers
39
UGCNETDec2015II6
Which of the following arguments are not valid ? "If Gora gets the job and works hard, then he will be promoted. if Gora gets promotion, then he will be happy. He will not be happy, therefore, either he will not get the job or he will not work hard." "Either Puneet is not ... $n^2 > 1$, then $n>1$. a and c b and c a,b, and c a and b
answered
Jun 6, 2019
in
Mathematical Logic
by
Satbir
Boss
(
24.2k
points)

1.5k
views
ugcnetdec2015ii
discretemathematics
mathematicallogic
+3
votes
1
answer
40
Mathematical Logic Ques:Self doubt
“Not every satisfiable logic is valid” Representation of it will be $1)\sim \left ( \forall S(x)\rightarrow V(x) \right )$ or $2)\sim \left ( \forall S(x)\vee V(x) \right )$ Among $1)$ and $2)$, which one is correct? and why?
asked
Jun 4, 2019
in
Mathematical Logic
by
srestha
Veteran
(
119k
points)

196
views
discretemathematics
mathematicallogic
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