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Recent questions in Discrete Mathematics

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1 answer

5221

Pankaj kumar asked in Mathematical Logic Sep 1, 2016

by Pankaj kumar

585 views

1 vote

2 answers

5222

test series
Which of the following arguments is invalid? $P \vee Q, \sim P \rightarrow R, Q \rightarrow S \vdash R \wedge S$ $P \rightarrow \sim Q, R \rightarrow Q, R \vdash \sim P$ $P \rightarrow R, Q \rightarrow R, Q \vee P \vdash R$ $P \rightarrow \sim Q, \sim Q \vdash P$

Pankaj kumar asked in Mathematical Logic Sep 1, 2016

by Pankaj kumar

750 views

28 votes

3 answers

5223

Find the number of integral solutions using generating function
Find the number of integral solutions of $\large 2x + y + z = 20$ with $x, y, z >= 0$ ? I tried finding coefficient of $x^{20}$ in $(1 + x^2 + x^3 + ...... + x^{10})(1+ x^2 + .......... + x^{20})^2$, but it gives wrong answer ?

mcjoshi asked in Combinatory Sep 1, 2016

9.1k views

0 votes

1 answer

5224

rank of a matrix
Rank of following matix? 12 22 32 42 32 42 52 62 42 52 62 72 please note the changes.

gate_forum asked in Mathematical Logic Aug 31, 2016

912 views

1 vote

0 answers

5225

#Generating_Function
We are interested in generating functions for the number of different ways to com pose a bag of n donuts subject to various restrictions. For each of the restrictions in below, find a closed form for the corresponding generating function. 1.The donuts must be chocolate, ... there must be a multiple of 4 plain. 2. All the donuts are plain and their number is a multiple of 4

Sarvottam Patel asked in Mathematical Logic Aug 31, 2016

by Sarvottam Patel

451 views

1 vote

3 answers

5226

Probability Expectaiton
A box contain 2 red balls and 3 white balls. The random experiment is picking two balls from the box. When 2 white balls picked, the balls will be replaced and experiment repeated. Otherwise stop the experiment. What is the expected number of repetations?

Manu Madhavan asked in Mathematical Logic Aug 31, 2016

by Manu Madhavan

584 views

1 vote

2 answers

5227

#Deragement How many ways we put letter
How many ways we can put 5 letters L1 ,L2, L3, L4 ,L5 in 5 envelope e1, e2, e3, e4, e5 (at 1 letter per envelope) so that At most 1 letter is correctly placed At least 1 Letter is wrongly placed

Sarvottam Patel asked in Mathematical Logic Aug 30, 2016

by Sarvottam Patel

648 views

2 votes

2 answers

5228

Permutation
Given a integer N greater than zero. How many sequences of 1's and 2's are there such that sum of the numbers in the sequence = N ? (not necessary that every sequence must contain both 1 and 2 ) example : for N = 2 ; 11,2 => ans = 2 sequences of 1's and 2's for N = 3 ; 11,12,21 => ans = 3 sequences of 1's and 2's

dd asked in Combinatory Aug 29, 2016

by dd

673 views

1 vote

1 answer

5229

GATEBOOK
Given answer a C but iam getting A

Niharika 1 asked in Mathematical Logic Aug 28, 2016

217 views

2 votes

1 answer

5230

Quiz Question
Which of the following interference system is invalid? $R \rightarrow S, \sim \vdash \sim R$ $\sim R, P \rightarrow Q, Q \rightarrow R \vdash \sim P$ ... Iam getting answer as c but given b.

Niharika 1 asked in Mathematical Logic Aug 28, 2016

637 views

2 votes

1 answer

5231

Group theory
Let the number of non-isomorphic groups of order 10 be X and number of non-isomorphic groups of order 24 be Y then the value of X and Y a) 3,2 b)2,7 c)1,7 d)4,5

Amit puri asked in Mathematical Logic Aug 27, 2016

418 views

2 votes

1 answer

5232

Group theory
Let $G$ be a group whose presentation is $G=\{ x, y \mid x^5 =y^2 =e, \:\:\:\: x^2y=yx\}$, $\mathcal{Z}_n$: Set of integers modulo $n$ Then $G$ is isomorphic to $\mathcal{Z}_5$ $\mathcal{Z}_{10}$ $\mathcal{Z}_2$ $\mathcal{Z}_{30}$

Amit puri asked in Mathematical Logic Aug 27, 2016

284 views

3 votes

2 answers

5233

Self
∀x∃y P(x) → Q(y) ≡ ∀x P(x) → ∃yQ(y) We have to prove whether this is a tautology or not. How do we proceed ?

bane asked in Mathematical Logic Aug 26, 2016

by bane

506 views

1 vote

2 answers

5234

wff
A WFF that is equivalent to the WFF x=>y is: (A) y=>x (B) ~y=>x (C) ~y=>~x (D) y=>~x

omveer asked in Mathematical Logic Aug 25, 2016

by omveer

1.4k views

4 votes

2 answers

5235

generalised pigeonhole principle
Show that if seven integers are selected from the first 10 positive integers, there must be at least two pairs of these integers with the sum 11. Attempt-:partition will be {(1,10),(2,9),(3,8)(4,7)(5,6)} now how to apply pigeonhole principle to find the answer?

sourav. asked in Combinatory Aug 24, 2016

2.1k views

1 vote

2 answers

5236

#Kenneth_Rossen
How many solutions are there to the equation x1+x2+x3+x4 =17 where xi is non negative? Please explain how this problem has 1 to 1 correspondence with the solution of reordering of 17 1's and 3 0's. How many solutions are there to the equation x1+x2+x3+x4+x5+x6 =29 where xi is non negative such that x1<=5?

Sarvottam Patel asked in Combinatory Aug 24, 2016

by Sarvottam Patel

822 views

1 vote

1 answer

5237

Counting
How many ways are there to seat six people around a circular table where two seatings are considered the same when everyone has the same two neighbors without regard to whether they are right or left neighbors? It would be better if one provide a pictorial explanation.

sourav. asked in Combinatory Aug 23, 2016

777 views

1 vote

2 answers

5238

UGC NET CSE | June 2011 | Part 2 | Question: 3
The proposition $\sim p \vee q$ is equivalent to $p \rightarrow q$ $q \rightarrow p$ $p \leftrightarrow q$ $p \vee q$

makhdoom ghaya asked in Mathematical Logic Aug 22, 2016

by makhdoom ghaya

488 views

3 votes

1 answer

5239

Graph theory
Let G be a graph with 10 vertices, and d(v) be the degree of a vertex v. The following conditions are holds for Graph G. 3 $\leq$ d (v) $\leq$ 5 for each vertex v in G. Not every vertex degree is even No two odd degree vertices are of the same ... be the number of edges, Y be the vertices having even degree and Z be the vertices having odd degree in G. Find the value of X+10Y+100Z?

Amit puri asked in Graph Theory Aug 22, 2016

630 views

2 votes

0 answers

5240

Counting Theory
10 Points were selected in the sequence with each side 1 unit, there will be atleast two points (of those points) such that distance between them can not exceeds.. 1/(2.sqrt(2)) (sqrt(2))/3 1/3 (sqrt(2))/9

rude asked in Combinatory Aug 22, 2016

by rude

349 views

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