Recent questions and answers in Mathematical Logic

+2 votes

1 answer

1

find close form of generating function discrete mathematics kenneth rosen

answered 2 days ago in Mathematical Logic by neeraj33negi (399 points) | 51 views

0 votes

1 answer

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.

answered 2 days ago in Mathematical Logic by Shubhgupta Junior (639 points) | 17 views

0 votes

0 answers

3

UGCNET-Nov-2017-III-70
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)]

asked 3 days ago in Mathematical Logic by Roma_nagpal (115 points) | 14 views

0 votes

0 answers

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?

asked 4 days ago in Mathematical Logic by Pratyush (7 points) | 24 views

+33 votes

7 answers

5

GATE2015-3-24
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

answered 4 days ago in Mathematical Logic by Ayush Upadhyaya Loyal (8.8k points) | 3.2k views

+22 votes

5 answers

6

GATE2008-IT-21
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 5 days ago in Mathematical Logic by Ayush Upadhyaya Loyal (8.8k points) | 2.4k views

+26 votes

6 answers

7

GATE2017-1-02
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

answered 6 days ago in Mathematical Logic by Ayush Upadhyaya Loyal (8.8k points) | 3.5k views

0 votes

2 answers

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 by Deepakk Poonia (Dee) Boss (13.2k points) | 32 views

+2 votes

3 answers

9

UGCNET-Dec2014-III-57
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 in Mathematical Logic by Prasanjeet Ghosh Active (1.3k points) | 571 views

+2 votes

3 answers

10

UGCNET-Dec2014-III-55
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 by Prasanjeet Ghosh Active (1.3k points) | 431 views

+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

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) Boss (13.2k points) | 51 views

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 by Deepakk Poonia (Dee) Boss (13.2k points) | 31 views

0 votes

0 answers

14

generating funtion
1/1−2x2 provide close formula for the sequences it determines

asked Jun 14 in Mathematical Logic by sunil sarode Active (1.1k points) | 14 views

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

Logic-Kenneth Rosen (Ex1.4-11f)
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

0 votes

0 answers

18

ISI 2014 MMA- 9

asked Jun 12 in Mathematical Logic by Sammohan Ganguly (417 points) | 21 views

0 votes

0 answers

19

ISI 2014 MMA - 3

asked Jun 12 in Mathematical Logic by Sammohan Ganguly (417 points) | 23 views

0 votes

2 answers

20

Sheldon ross -Conditional probability

answered Jun 12 in Mathematical Logic by Shaik Masthan Active (2.5k points) | 66 views

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 points) | 72 views

+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 points) | 65 views

0 votes

0 answers

23

Logic-Kenneth Rosen(Ex1.4-5e)
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

0 votes

0 answers

24

Logic-Kenneth Rosen(Ex1.3-57)
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

0 votes

0 answers

25

Self-Doubt-Logic
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

0 votes

1 answer

26

Distinguishable objects and indistinguishable boxes

answered Jun 8 in Mathematical Logic by Deepakk Poonia (Dee) Boss (13.2k points) | 75 views

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 points) | 78 views

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

+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 by Deepakk Poonia (Dee) Boss (13.2k points) | 72 views

+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) Boss (13.2k points) | 39 views

0 votes

2 answers

31

Express the statement in logical expression

answered Jun 5 in Mathematical Logic by Deepakk Poonia (Dee) Boss (13.2k points) | 301 views

+1 vote

1 answer

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 by Deepakk Poonia (Dee) Boss (13.2k points) | 69 views

0 votes

0 answers

33

Sheldon ross(9th ed.)-chapter 2 example 5(g)

asked Jun 4 in Mathematical Logic by Prateek Raghuvanshi Active (3.9k points) | 23 views

0 votes

0 answers

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

0 votes

2 answers

35

Number of ordered pairs

answered Jun 1 in Mathematical Logic by Deepakk Poonia (Dee) Boss (13.2k points) | 46 views

0 votes

1 answer

36

Test series
How to do these type of questions?

answered Jun 1 in Mathematical Logic by Deepakk Poonia (Dee) Boss (13.2k points) | 48 views

0 votes

1 answer

37

Made easy test

answered May 31 in Mathematical Logic by Deepakk Poonia (Dee) Boss (13.2k points) | 52 views

0 votes

1 answer

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 Loyal (8.2k points) | 49 views

0 votes

1 answer

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 Loyal (8.2k points) | 19 views

0 votes

1 answer

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 by Kushagra Chatterjee Loyal (8.2k points) | 15 views

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