Recent questions and answers in Mathematical Logic - GATE CSE Doubts

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Kenneth H. Rosen 7th edition
Show that ¬(p ⊕ q) and p ↔ q are logically equivalent.

asked 6 days ago in Mathematical Logic by Champa (5 points) | 5 views

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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)

answered Mar 22 in Mathematical Logic by zxy123 (3.6k points) | 16 views

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Kenneth H Rosen
Show that $p<-->q$ and ~p <-->~q are logically equivalent.

answered Mar 22 in Mathematical Logic by zxy123 (3.6k points) | 17 views

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Discrete Mathematics and its applications (Kenneth Rosen)

asked Mar 22 in Mathematical Logic by SmeetPatel (5 points) | 18 views

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Prepositional Logic
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 by hitendra singh (73 points) | 16 views

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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

asked Mar 7 in Mathematical Logic by donniedarko (39 points) | 34 views

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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)

asked Feb 9 in Mathematical Logic by s_dr_13 (15 points) | 18 views

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Ace Test Series
Is the group closed under monoid? Can we treat 1 as identity??

asked Feb 3 in Mathematical Logic by vipin.gautam1906 (9 points) | 24 views

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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.

answered Jan 23 in Mathematical Logic by zxy123 (3.6k points) | 31 views

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How decision making is done in Lisp?
How decision making is done in Lisp?

asked Jan 17 in Mathematical Logic by Vikash40203 (5 points) | 15 views

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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

asked Jan 16 in Mathematical Logic by hadarsh (5 points) | 19 views

+1 vote

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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.

asked Jan 14 in Mathematical Logic by donniedarko (39 points) | 26 views

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made easy test series
please explain iam unable understand this

answered Jan 10 in Mathematical Logic by Shaik Masthan (1.5k points) | 31 views

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Ace Test Series

answered Jan 4 in Mathematical Logic by wayward_blu (11 points) | 27 views

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Made easy 2018 postal study course
Why is the answer is d)? I guess it should be a) can someone explain please

asked Dec 28, 2020 in Mathematical Logic by Anshul purohit (5 points) | 21 views

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Made easy Full length Test series FST2 2021 doubt on set theory

answered Dec 24, 2020 in Mathematical Logic by toxicdesire (555 points) | 25 views

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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) ) )

asked Dec 22, 2020 in Mathematical Logic by yashhoskere (5 points) | 27 views

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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

answered Dec 22, 2020 in Mathematical Logic by ankitgupta.1729 (357 points) | 45 views

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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]

asked Dec 4, 2020 in Mathematical Logic by Mellophi (363 points) | 18 views

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Kenneth H Rosen
What is the meaning of all the four options? Please explain in detail.

answered Nov 28, 2020 in Mathematical Logic by zxy123 (3.6k points) | 38 views

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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.

asked Nov 28, 2020 in Mathematical Logic by neel19 (7 points) | 21 views

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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?

asked Nov 21, 2020 in Mathematical Logic by Marwa-jami (5 points) | 25 views

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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)

asked Nov 17, 2020 in Mathematical Logic by Marwa-jami (5 points) | 19 views

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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.

answered Nov 11, 2020 in Mathematical Logic by zxy123 (3.6k points) | 45 views

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Linear Algebra
Is there vector space in syllabus now?

answered Nov 10, 2020 in Mathematical Logic by SarathBaswa (849 points) | 20 views

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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 ).

asked Nov 4, 2020 in Mathematical Logic by jeekpon (5 points) | 19 views

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Probability Distributions
From where should i learn probability distributions ?

asked Oct 30, 2020 in Mathematical Logic by kaleen bhaiya (9 points) | 20 views

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First order logic
Is this first order logic Valid ? [ β→ ∃ₓ α(x) ]→ [ ∀ₓ(β→α(x)) ]

answered Oct 27, 2020 in Mathematical Logic by gatecse (241 points) | 37 views

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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.

asked Oct 25, 2020 in Mathematical Logic by Sinchit (17 points) | 40 views

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Probability # Self doubt # GO test
How to solve this calculation step by step ? Ans is 99.56%.

asked Oct 22, 2020 in Mathematical Logic by Sharma9999999 (5 points) | 20 views

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#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 ... $a_{n} = 2a_{n-1} + a_{n-2}$ $a_{n} = a_{n-1} + a_{n-3}$

answered Oct 14, 2020 in Mathematical Logic by mayureshpatle (861 points) | 30 views

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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.

asked Oct 11, 2020 in Mathematical Logic by Rishav Chetan (9 points) | 21 views

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# Made Easy test

asked Oct 11, 2020 in Mathematical Logic by raviranjan21 (13 points) | 26 views

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Self Doubt - Previous Year Question.
Is the conversion from Ǝx [P(x) ˄ Q(x)] to Ǝx P(x) ˄ Ǝx Q(x) valid?

answered Oct 9, 2020 in Mathematical Logic by iarnav (231 points) | 22 views

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My College Notes
What are Relative Sets? Please explain with example

asked Oct 7, 2020 in Mathematical Logic by ivarnam (5 points) | 13 views

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Kenneth Rosen specific sections
Hi, I have been referring to Kenneth Rosen for Discrete Mathematics for GATE 2021 and since I have less time left, I would like to know which specific sections are to be read from the chapters in syllabus. I already know we have to go through ... or just some part of these chapters? If specific parts are to be completed can you please guide me with it? Thank you

asked Oct 3, 2020 in Mathematical Logic by motabhai (5 points) | 29 views

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Gatebook test series
Why option B is not correct here ? B’coz he can be a politician as he thinks about politics.

asked Sep 30, 2020 in Mathematical Logic by Raj_81 (23 points) | 40 views

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Combinatorics and Propositional logic
Which book should i refer for Combinatorics and Propositional logic?

asked Sep 22, 2020 in Mathematical Logic by kaleen bhaiya (9 points) | 23 views

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NPTEL DISCRETE STRUCTURE ASSIGNMENT QUESTION
Which of the following are logical consequences of { ($\alpha$ → $\beta$’), $\beta$, ($\gamma$ ’ → $\alpha$) } ($\alpha$ → $\beta$’) $\beta$’ $\gamma$ $\alpha$ Answer given is C but if this question asked as MSQ question then can A be the possible answer??

answered Sep 19, 2020 in Mathematical Logic by Ehraz Hasan (366 points) | 69 views

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Test series: GATE academy Logarithms question 2

answered Aug 23, 2020 in Mathematical Logic by mandeepC (1k points) | 35 views

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Recent questions and answers in Mathematical Logic

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