# Recent questions and answers in Mathematical Logic

1 vote
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?
Series solution of $(2^k) \times 1 + (2^{k-1}) \times 2+ (2^{k-2}) \times 3+…+(2^2) \times(n-2) +2(n-1) +n?$
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 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
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 ?
A= {{}} and B = { ϕ } is A and B are equal set? please answer with explaination.
Show that ¬(p ⊕ q) and p ↔ q are logically equivalent.
1 vote
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)
Show that $p<-->q$ and ~p <-->~q are logically equivalent.
is section 7.2 n-ary relations and their applications given in kenneth rosen included or important for gate preparation??
which of the following is valid ? 1- p => ( q v r ) 2- p => ( q ^ r ) please provide little bit explaination?
1 vote
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
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 $S$
1 vote
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
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)
Is the group closed under monoid? Can we treat 1 as identity??
1 vote
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.
How decision making is done in Lisp?
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
1 vote
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.
please explain iam unable understand this
Why is the answer is d)? I guess it should be a) can someone explain please
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?
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) ) )
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
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.
What is the meaning of all the four options? Please explain in detail.
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.
A)T B) F C) T D) F E) T F) T G) F H) T Are these truth values that I assigned correct?
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)
1 vote
S1 is True , S2 is True. S1 is True , S2 is False. S1 is False , S2 is True. S1 is False , S2 is False.
Is there vector space in syllabus now?
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 ).
From where should i learn probability distributions ?
Is this first order logic Valid ? [ β→ ∃ₓ α(x) ]→ [ ∀ₓ(β→α(x)) ]
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 ... $a_{n} = 2a_{n-1} + a_{n-2}$ $a_{n} = a_{n-1} + a_{n-3}$