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Recent questions and answers in Mathematical Logic

Recent questions and answers in Mathematical Logic

1 vote
0 answers 11 views
#self_doubt #graph_theory
If a Graph G is Eulerian then all nodes will have Even degree But is the reverse True i.e. for any graph G’ if nodes of G’ have even degrees then G’ is Eulerian?
If a Graph G is Eulerian then all nodes will have Even degree But is the reverse True i.e. for any graph G’ if nodes of G’ have even degrees then G’ is Eulerian?
asked Jun 3 in Mathematical Logic Palash Nandi 1 13 points 11 views
0 votes
1 answer 22 views
Series solution
Series solution of $(2^k) \times 1 + (2^{k-1}) \times 2+ (2^{k-2}) \times 3+…+(2^2) \times(n-2) +2(n-1) +n?$
Series solution of $(2^k) \times 1 + (2^{k-1}) \times 2+ (2^{k-2}) \times 3+…+(2^2) \times(n-2) +2(n-1) +n?$
answered May 13 in Mathematical Logic Nikhil_dhama 225 points 22 views
0 votes
0 answers 11 views
PhD Admissions Written Test (Basic)
Consider the matrix A = ( 1 1 7 2 −4 14 3 1 21 ) and let vA ={x y z } be vector not containing all 0s. The product A vA is 0 (all 0s) if we set x, y, z as how to solve such question
Consider the matrix A = ( 1 1 7 2 −4 14 3 1 21 ) and let vA ={x y z } be vector not containing all 0s. The product A vA is 0 (all 0s) if we set x, y, z as how to solve such question
asked May 2 in Mathematical Logic Rashimdixit 9 points 11 views
0 votes
0 answers 8 views
PhD Admissions Written Test (Basic)
Consider the following on-line learning method to estimate the expected value of a real-valued random variable X. We begin with an initial estimate µ0, and then for t = 1, 2, . . . , Obtain xt as an independent identical distribution (i.i.d) sample of X ... t. Assume X is normally distributed with mean µ and variance σ 2 . If we choose αt = 1 t , then E[µt ] is
Consider the following on-line learning method to estimate the expected value of a real-valued random variable X. We begin with an initial estimate µ0, and then for t = 1, 2, . . . , Obtain xt as an independent identical distribution (i.i.d) sample of X, and Revise our ... at step t. Assume X is normally distributed with mean µ and variance σ 2 . If we choose αt = 1 t , then E[µt ] is
asked Apr 26 in Mathematical Logic Rashimdixit 9 points 8 views
0 votes
0 answers 8 views
Combinatorics
I am not able to solve few combinatroics questions although I have solve decent number of questions but sometimes not able to crack if a new type of sums comes up.. What to do ? How to proceed ?
I am not able to solve few combinatroics questions although I have solve decent number of questions but sometimes not able to crack if a new type of sums comes up.. What to do ? How to proceed ?
asked Apr 25 in Mathematical Logic exceptionXD 5 points 8 views
0 votes
1 answer 31 views
Self Doubt Set Theory
A= {{}} and B = { ϕ } is A and B are equal set? please answer with explaination.
A= {{}} and B = { ϕ } is A and B are equal set? please answer with explaination.
answered Apr 25 in Mathematical Logic raun220 23 points 31 views
0 votes
0 answers 18 views
Kenneth H. Rosen 7th edition
Show that ¬(p ⊕ q) and p ↔ q are logically equivalent.
Show that ¬(p ⊕ q) and p ↔ q are logically equivalent.
asked Apr 7 in Mathematical Logic Champa 5 points 18 views
1 vote
1 answer 37 views
Kenneth H Rosen
Let p and q be propositions p: I bought a lottery ticket this week q: I won the million-dollar jackpot Express each of these propositions as English sentences (i) ~p (ii) p$\vee$q (iii) p$\rightarrow$q (iv) p$\wedge$q (v) p$\Leftrightarrow$q (vi) ~p$\rightarrow$~q (vii) ~p$\wedge$~q (viii) ~p$\vee$(p$\wedge$q)
Let p and q be propositions p: I bought a lottery ticket this week q: I won the million-dollar jackpot Express each of these propositions as English sentences (i) ~p (ii) p$\vee$q (iii) p$\rightarrow$q (iv) p$\wedge$q (v) p$\Leftrightarrow$q (vi) ~p$\rightarrow$~q (vii) ~p$\wedge$~q (viii) ~p$\vee$(p$\wedge$q)
answered Mar 22 in Mathematical Logic zxy123 3.6k points 37 views
0 votes
1 answer 36 views
Kenneth H Rosen
Show that $p<-->q$ and ~p <-->~q are logically equivalent.
Show that $p<-->q$ and ~p <-->~q are logically equivalent.
answered Mar 22 in Mathematical Logic zxy123 3.6k points 36 views
0 votes
0 answers 23 views
Discrete Mathematics and its applications (Kenneth Rosen)
is section 7.2 n-ary relations and their applications given in kenneth rosen included or important for gate preparation??
asked Mar 22 in Mathematical Logic SmeetPatel 5 points 23 views
0 votes
0 answers 19 views
Prepositional Logic
which of the following is valid ? 1- p => ( q v r ) 2- p => ( q ^ r ) please provide little bit explaination?
which of the following is valid ? 1- p => ( q v r ) 2- p => ( q ^ r ) please provide little bit explaination?
asked Mar 9 in Mathematical Logic hitendra singh 73 points 19 views
1 vote
0 answers 40 views
GATE functions and relations
The function f: [0,3]$\rightarrow$[1,29] defined by f(x) = $2x^{3} - 15x^{2} + 36x +1$ where x is an integer is (a) injective and surjective (b) surjective but not injective (C) injective but not surjective (d) neither injective not surjective
The function f: [0,3]$\rightarrow$[1,29] defined by f(x) = $2x^{3} - 15x^{2} + 36x +1$ where x is an integer is (a) injective and surjective (b) surjective but not injective (C) injective but not surjective (d) neither injective not surjective
asked Mar 7 in Mathematical Logic donniedarko 39 points 40 views
3 votes
3 answers 715 views
GATE CSE 2021 Set 2 | Question: 15 | Video Solution
Choose the correct choice(s) regarding the following proportional logic assertion $S$: $S: (( P \wedge Q) \rightarrow R) \rightarrow (( P \wedge Q) \rightarrow (Q \rightarrow R))$ $S$ is neither a tautology nor a contradiction $S$ is a tautology $S$ is a contradiction The antecedent of $S$ is logically equivalent to the consequent of $S$
asked Feb 18 in Mathematical Logic Arjun 257 points 715 views
1 vote
4 answers 512 views
GATE CSE 2021 Set 1 | Question: 7 | Video Solution
Let $p$ and $q$ be two propositions. Consider the following two formulae in propositional logic. $S_1: (\neg p\wedge(p\vee q))\rightarrow q$ $S_2: q\rightarrow(\neg p\wedge(p\vee q))$ Which one of the following choices is correct? Both $S_1$ and $S_2$ are tautologies ... tautology but $S_2$ is not a tautology $S_1$ is not a tautology but $S_2$ is a tautology Neither $S_1$ nor $S_2$ is a tautology
asked Feb 18 in Mathematical Logic Arjun 257 points 512 views
0 votes
0 answers 21 views
SELF DOUBT IN IMPLICATIONS
Can anybody please make me understand what's the relationship among implications in proposition logic and statements such as 1. Necessarily but not sufficient 2. Sufficient but not necessary 3. Sufficient as well as necessary 4. Neither sufficient nor necessary ( although I am ... <--> q If p is neither sufficient nor necessary is the same as ! (p <--> q)
Can anybody please make me understand what's the relationship among implications in proposition logic and statements such as 1. Necessarily but not sufficient 2. Sufficient but not necessary 3. Sufficient as well as necessary 4. Neither sufficient nor necessary ( although I am skeptical about this specific ... is same as p <--> q If p is neither sufficient nor necessary is the same as ! (p <--> q)
asked Feb 9 in Mathematical Logic s_dr_13 15 points 21 views
0 votes
0 answers 28 views
Ace Test Series
Is the group closed under monoid? Can we treat 1 as identity??
Is the group closed under monoid? Can we treat 1 as identity??
asked Feb 3 in Mathematical Logic vipin.gautam1906 9 points 28 views
1 vote
1 answer 38 views
Probablity engineering mathematics
A box contains 10 apples out of which 4 are rotten. Two apples are taken out together if one of them is good what is the probablity that the other one is also good. Note: Please don’t use ‘C’ combination terms in your answer rather try to make it as clear as possible.
A box contains 10 apples out of which 4 are rotten. Two apples are taken out together if one of them is good what is the probablity that the other one is also good. Note: Please don’t use ‘C’ combination terms in your answer rather try to make it as clear as possible.
answered Jan 23 in Mathematical Logic zxy123 3.6k points 38 views
0 votes
0 answers 17 views
How decision making is done in Lisp?
How decision making is done in Lisp?
How decision making is done in Lisp?
asked Jan 17 in Mathematical Logic Vikash40203 5 points 17 views
0 votes
0 answers 21 views
Gate overflow book
I am having a confusion in precedence order of logical operators. For e.g. consider the expression (a ∧ b) → (a ∧ c) ∨ d. Then how is the expression evaluated? Like is it ((a ∧ b) → (a ∧ c)) ∨ d or (a ∧ b) →((a ∧ c) ∨ d)? ... than implication, so the second one should be correct. But from the solution, I see it is the first one. Link to the question: https://gateoverflow.in/654
I am having a confusion in precedence order of logical operators. For e.g. consider the expression (a ∧ b) → (a ∧ c) ∨ d. Then how is the expression evaluated? Like is it ((a ∧ b) → (a ∧ c)) ∨ d or (a ∧ b) →((a ∧ c) ∨ d)? I read ... precedence than implication, so the second one should be correct. But from the solution, I see it is the first one. Link to the question: https://gateoverflow.in/654
asked Jan 16 in Mathematical Logic hadarsh 5 points 21 views
1 vote
0 answers 29 views
Self-doubt sum series and logaritms.
These are what i ended up with while solving a couple of recurrance relation can anyone help to solve further. $(n^2) log(n/2^{k-1}) + 2(n^2) log(n/2^{k-2}) + 3(n^2) log(n/2^{k-3}) + ...+ (n^2) log(n)$ $2. lg n + lg (n / 2) + lg (n / 4) + ... + lg (n / 2^{lg n})$ Note: Assume base 2 for log terms.
These are what i ended up with while solving a couple of recurrance relation can anyone help to solve further. $(n^2) log(n/2^{k-1}) + 2(n^2) log(n/2^{k-2}) + 3(n^2) log(n/2^{k-3}) + ...+ (n^2) log(n)$ $2. lg n + lg (n / 2) + lg (n / 4) + ... + lg (n / 2^{lg n})$ Note: Assume base 2 for log terms.
asked Jan 14 in Mathematical Logic donniedarko 39 points 29 views
0 votes
1 answer 34 views
made easy test series
please explain iam unable understand this
please explain iam unable understand this
answered Jan 10 in Mathematical Logic Shaik Masthan 1.6k points 34 views
0 votes
1 answer 29 views
Ace Test Series
answered Jan 4 in Mathematical Logic wayward_blu 11 points 29 views
0 votes
0 answers 22 views
Made easy 2018 postal study course
Why is the answer is d)? I guess it should be a) can someone explain please
Why is the answer is d)? I guess it should be a) can someone explain please
asked Dec 28, 2020 in Mathematical Logic Anshul purohit 5 points 22 views
0 votes
1 answer 26 views
Made easy Full length Test series FST2 2021 doubt on set theory
Which of the options are correct? 85 students passed in at least 2 subjects 55 students passed in at least 2 subjects 30 students passed in all subjects 55 students passed in all the subjects how to solve this one?
answered Dec 24, 2020 in Mathematical Logic toxicdesire 555 points 26 views
0 votes
0 answers 31 views
propositional logic
Let say the statement is ∀ t ( t ∈ r ( p(t) ) ) Now ( ∀ t ) can also be written as ( ~ ~ ∀ t ) if i push one negation inside then it becomes ~∃ t ~ , now my doubt is when it passes through belongs to ( ∈ ) 1. Can it leave it like that itself and move inside without making it ∉. 2. If the ... negation ∃ t ( t ∉ r ( ~ p(t) ) ) or ∃ t ( t ∈ r ( ~ p(t) ) ) or ∃ t ( t ∉ r ( p(t) ) )
Let say the statement is ∀ t ( t ∈ r ( p(t) ) ) Now ( ∀ t ) can also be written as ( ~ ~ ∀ t ) if i push one negation inside then it becomes ~∃ t ~ , now my doubt is when it passes through belongs to ( ∈ ) 1. Can it leave it like that itself and move inside without making it ∉. 2. If the negation ... pushing negation ∃ t ( t ∉ r ( ~ p(t) ) ) or ∃ t ( t ∈ r ( ~ p(t) ) ) or ∃ t ( t ∉ r ( p(t) ) )
asked Dec 22, 2020 in Mathematical Logic yashhoskere 5 points 31 views
0 votes
1 answer 49 views
UGC NET DEC 2019 question
Let $a^{2c} \enspace mod \enspace n = (a^c)^2\enspace mod\enspace n$ and $a^{2c+1} \enspace mod \enspace n = a(a^c)^2\enspace mod\enspace n$ $For \enspace a =7, b=17 \enspace and \enspace n=561.$ what is the value of $a^b(mod\enspace n)$ ? 160 166 157 67
Let $a^{2c} \enspace mod \enspace n = (a^c)^2\enspace mod\enspace n$ and $a^{2c+1} \enspace mod \enspace n = a(a^c)^2\enspace mod\enspace n$ $For \enspace a =7, b=17 \enspace and \enspace n=561.$ what is the value of $a^b(mod\enspace n)$ ? 160 166 157 67
answered Dec 22, 2020 in Mathematical Logic ankitgupta.1729 357 points 49 views
0 votes
0 answers 19 views
Self Doubt - Probabilty
If the probability of getting a head is P then what is the number of times we need to toss the coin to get a head. [closed]
If the probability of getting a head is P then what is the number of times we need to toss the coin to get a head.
asked Dec 4, 2020 in Mathematical Logic Mellophi 363 points 19 views
0 votes
1 answer 40 views
Kenneth H Rosen
What is the meaning of all the four options? Please explain in detail.
What is the meaning of all the four options? Please explain in detail.
answered Nov 28, 2020 in Mathematical Logic zxy123 3.6k points 40 views
0 votes
0 answers 23 views
Which sub topics to study?
I have not studied 11 and 12 std maths in much depth and, as a result, I am too weak in 12 topics. I want to know which sub-topics do I have to study from 11 and 12 std. I was solving PYQ on integration and found some problems have double ... point. So, can anyone give me the topic list or the chapters which I have to study from NCERT. It will be of great help.
I have not studied 11 and 12 std maths in much depth and, as a result, I am too weak in 12 topics. I want to know which sub-topics do I have to study from 11 and 12 std. I was solving PYQ on integration and found some problems have double integration in ... the point. So, can anyone give me the topic list or the chapters which I have to study from NCERT. It will be of great help.
asked Nov 28, 2020 in Mathematical Logic neel19 7 points 23 views
0 votes
0 answers 26 views
Could not found the source
A)T B) F C) T D) F E) T F) T G) F H) T Are these truth values that I assigned correct?
A)T B) F C) T D) F E) T F) T G) F H) T Are these truth values that I assigned correct?
asked Nov 21, 2020 in Mathematical Logic Marwa-jami 5 points 26 views
0 votes
0 answers 20 views
A site on google
Which of the following formulas represents the sentence, 'Share prices will go up, and if interest rates go up too, there will be a recession', where; p means 'share prices will go up' q means 'interest rates will go up' r means 'there will be a recession'. A) (p ∧ q) →r B) p∧( q →r)
Which of the following formulas represents the sentence, 'Share prices will go up, and if interest rates go up too, there will be a recession', where; p means 'share prices will go up' q means 'interest rates will go up' r means 'there will be a recession'. A) (p ∧ q) →r B) p∧( q →r)
asked Nov 17, 2020 in Mathematical Logic Marwa-jami 5 points 20 views
1 vote
1 answer 51 views
Applied gate testseries
S1 is True , S2 is True. S1 is True , S2 is False. S1 is False , S2 is True. S1 is False , S2 is False.
S1 is True , S2 is True. S1 is True , S2 is False. S1 is False , S2 is True. S1 is False , S2 is False.
answered Nov 11, 2020 in Mathematical Logic zxy123 3.6k points 51 views
0 votes
1 answer 23 views
Linear Algebra
Is there vector space in syllabus now?
Is there vector space in syllabus now?
answered Nov 10, 2020 in Mathematical Logic SarathBaswa 849 points 23 views
0 votes
0 answers 21 views
Mathematics for Computer Science
Let S be a sequence of N numbers containing n distinct positive integers. Prove that if N ≥ 2^n then S has a consecutive subsequence whose product is a perfect square using the pigeonhole principle. (e.g., (3,4,2,3,3,4,2,4) contains a consecutive subsequence whose product equals 24^2 ).
Let S be a sequence of N numbers containing n distinct positive integers. Prove that if N ≥ 2^n then S has a consecutive subsequence whose product is a perfect square using the pigeonhole principle. (e.g., (3,4,2,3,3,4,2,4) contains a consecutive subsequence whose product equals 24^2 ).
asked Nov 4, 2020 in Mathematical Logic jeekpon 5 points 21 views
0 votes
0 answers 21 views
Probability Distributions
From where should i learn probability distributions ?
From where should i learn probability distributions ?
asked Oct 30, 2020 in Mathematical Logic kaleen bhaiya 9 points 21 views
0 votes
1 answer 38 views
First order logic
Is this first order logic Valid ? [ β→ ∃ₓ α(x) ]→ [ ∀ₓ(β→α(x)) ]
Is this first order logic Valid ? [ β→ ∃ₓ α(x) ]→ [ ∀ₓ(β→α(x)) ]
answered Oct 27, 2020 in Mathematical Logic gatecse 247 points 38 views
0 votes
0 answers 53 views
Recurrence Relation
In a second degree non homogenous recurrence Relation let it be (an) -4(an-1)+4(an-2)= 2 • b^n Let m1 and m2 are the roots of the characteristic equation that is m1 = m2 =2. What will be the particular solution ? 1. ( A n^2 b^n )where A is an arbitrary constant. 2. ( A b^n ) where A is an arbitrary constant 3. None of the above.
In a second degree non homogenous recurrence Relation let it be (an) -4(an-1)+4(an-2)= 2 • b^n Let m1 and m2 are the roots of the characteristic equation that is m1 = m2 =2. What will be the particular solution ? 1. ( A n^2 b^n )where A is an arbitrary constant. 2. ( A b^n ) where A is an arbitrary constant 3. None of the above.
asked Oct 25, 2020 in Mathematical Logic Sinchit 17 points 53 views
0 votes
0 answers 21 views
Probability # Self doubt # GO test
How to solve this calculation step by step ? Ans is 99.56%.
How to solve this calculation step by step ? Ans is 99.56%.
asked Oct 22, 2020 in Mathematical Logic Sharma9999999 5 points 21 views
0 votes
1 answer 34 views
#Ace2019TestSeries
Messagees are transmitted over a communication channel using two signals. the transmission of one signal requires 1 microsecond and the transmission of the other requires two microseconds. the recurrence relation for the numver of different massages consisting of sequences of these two signals ( where each signal is ... $a_{n} = 2a_{n-1} + a_{n-2}$ $a_{n} = a_{n-1} + a_{n-3}$
Messagees are transmitted over a communication channel using two signals. the transmission of one signal requires 1 microsecond and the transmission of the other requires two microseconds. the recurrence relation for the numver of different massages consisting of sequences of these two signals ( where each signal is immediate followed ... $a_{n} = 2a_{n-1} + a_{n-2}$ $a_{n} = a_{n-1} + a_{n-3}$
answered Oct 14, 2020 in Mathematical Logic mayureshpatle 861 points 34 views
0 votes
0 answers 27 views
Previous year gate question (2003)
Consider the following formula a and its two interpretations I1 and I2 Which of the following statements is true? A I1 satisfies α, I2 does not B I2 satisfies α, I1 does not C Neither I2 nor I1 satisfies α D Both I1 and I2 satisfy α An explanation would be helpful.
Consider the following formula a and its two interpretations I1 and I2 Which of the following statements is true? A I1 satisfies α, I2 does not B I2 satisfies α, I1 does not C Neither I2 nor I1 satisfies α D Both I1 and I2 satisfy α An explanation would be helpful.
asked Oct 11, 2020 in Mathematical Logic Rishav Chetan 9 points 27 views
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