GATE Overflow - Recent questions in Discrete Mathematics
http://gateoverflow.in/questions/mathematics/discrete-mathematics
Powered by Question2AnswerUniform distribution
http://gateoverflow.in/145844/uniform-distribution
Assume that in a traffic junction the cycle of the traffic signal lights in 2 minutes of green(vehicle does not stop) and 3 minutes of red(vehicle stops). Consider that the arrival time of vehicles at the junction is uniformly distributed over 5 minute cycle. The expected waiting time (in minutes) for the vehicle at the junction is?Mathematical Logichttp://gateoverflow.in/145844/uniform-distributionSun, 20 Aug 2017 16:51:58 +0000Generating function
http://gateoverflow.in/145817/generating-function
What is the best source to study generating function in discrete mathematicsMathematical Logichttp://gateoverflow.in/145817/generating-functionSun, 20 Aug 2017 15:35:16 +0000Gate ee question
http://gateoverflow.in/145794/gate-ee-question
Let X be a random variable with probability density function <br />
<br />
F(x) ={<br />
<br />
0.2 for |x|<=1<br />
<br />
0.1 for 1<|x|<=4<br />
<br />
0 otherwise} <br />
<br />
The probability P(0.5<X<5) is? <br />
<br />
What is the relevance of mod here?Mathematical Logichttp://gateoverflow.in/145794/gate-ee-questionSun, 20 Aug 2017 14:27:44 +0000Poisson distribution
http://gateoverflow.in/145786/poisson-distribution
The second moment of a poisson distributed random variable is 2 the mean of the random variable is?Mathematical Logichttp://gateoverflow.in/145786/poisson-distributionSun, 20 Aug 2017 13:55:24 +00001995_13
http://gateoverflow.in/145776/1995_13
Mathematical Logichttp://gateoverflow.in/145776/1995_13Sun, 20 Aug 2017 12:54:50 +0000Probability
http://gateoverflow.in/145685/probability
What is the best video lecture for probability which covers all type of questions asked in gate??Mathematical Logichttp://gateoverflow.in/145685/probabilitySun, 20 Aug 2017 08:03:48 +0000Discrete mathematics
http://gateoverflow.in/145668/discrete-mathematics
what will be the number of even permutations of n objects? <br />
<br />
Explain!Combinatoryhttp://gateoverflow.in/145668/discrete-mathematicsSun, 20 Aug 2017 06:14:05 +0000Mathematical logic
http://gateoverflow.in/145641/mathematical-logic
Principal conjunctive normal form of ( p^ q)or( !p^ q) is<br />
<br />
a) sum of products<br />
<br />
b) product of sums<br />
<br />
c)sum of max terms<br />
<br />
d) product of max termsMathematical Logichttp://gateoverflow.in/145641/mathematical-logicSun, 20 Aug 2017 03:24:16 +0000Graph theory.
http://gateoverflow.in/145557/graph-theory
Matching and edge coloring are same ?Graph Theoryhttp://gateoverflow.in/145557/graph-theorySat, 19 Aug 2017 15:08:03 +0000Kenneth Rosen section 3.4 Exercise question 12
http://gateoverflow.in/145507/kenneth-rosen-section-3-4-exercise-question-12
<p>Is this approach right in proving a theorem </p>
<p><strong>Ques</strong>: show that a mod m = b mod m if a is congruent to b (mod m)</p>
<p><strong>Proof</strong>: given a is congruent to b(mod m)</p>
<p>According to definition:
<br>
a - b / m
<br>
i.e a - b = mx (for some integer x). ....(1)</p>
<p>Also a = mx + b
<br>
that can also be written as a mod m = b ...(2)</p>
<p>Also again from equation (1)</p>
<p>-b = mx - a
<br>
b = -mx + a
<br>
Or b = m(-x) + a
<br>
Or b = my + a ...(3)</p>
<p>Therefore b mod m = a </p>
<p>If we replace b in equation (2) by equation (3) then we get </p>
<p>a mod m = my + a
<br>
my + a can also be written as b mod m </p>
<p>Therefore, a mod m = b mod m </p>Set Theory & Algebrahttp://gateoverflow.in/145507/kenneth-rosen-section-3-4-exercise-question-12Sat, 19 Aug 2017 11:23:01 +0000SELF DOUBT
http://gateoverflow.in/145488/self-doubt
Explain isomorphism in context of groups with exampleGraph Theoryhttp://gateoverflow.in/145488/self-doubtSat, 19 Aug 2017 10:34:19 +0000Propositional function doubt
http://gateoverflow.in/145315/propositional-function-doubt
The Number of n-variable propositional function ?<br />
<br />
a. 2^2^n.<br />
<br />
b.2^n^2<br />
<br />
c.2^n<br />
<br />
d. n^2<br />
<br />
Can any one please explain the what should be the answer and how to get it?Mathematical Logichttp://gateoverflow.in/145315/propositional-function-doubtFri, 18 Aug 2017 18:07:26 +0000solution of rosen
http://gateoverflow.in/145129/solution-of-rosen
can anyone has the soft copy of kenneth h rosen solutions?Mathematical Logichttp://gateoverflow.in/145129/solution-of-rosenFri, 18 Aug 2017 06:40:06 +0000number of comparison
http://gateoverflow.in/145116/number-of-comparison
how many comparison are needed to locate the maximum and minimum in a sequence with 128 elements?Mathematical Logichttp://gateoverflow.in/145116/number-of-comparisonFri, 18 Aug 2017 05:56:24 +0000Mott Kandel Baker Ex. 1.7 Q. 23
http://gateoverflow.in/145084/mott-kandel-baker-ex-1-7-q-23
The circumference of two concentric disks is divided into 200 sections each. For the outer disk, 100 of the sections are painted red and 100 are painted white. For the inner disk, the sections are painted red or white in an arbitrary manner. Show that it is possible to align the 2 disks so that 100 or more of the sections of inner disk have their colors matched with the corresponding sections on the outer disk.Mathematical Logichttp://gateoverflow.in/145084/mott-kandel-baker-ex-1-7-q-23Fri, 18 Aug 2017 03:56:03 +0000Min Cut set
http://gateoverflow.in/145083/min-cut-set
<p><img alt="" src="http://gateoverflow.in/?qa=blob&qa_blobid=731647461265627009"></p>Graph Theoryhttp://gateoverflow.in/145083/min-cut-setFri, 18 Aug 2017 03:45:25 +0000Directed graph
http://gateoverflow.in/144967/directed-graph
how to calculate number of directed graphs possible having n vertices?Graph Theoryhttp://gateoverflow.in/144967/directed-graphThu, 17 Aug 2017 15:03:20 +0000rosen example 20
http://gateoverflow.in/144877/rosen-example-20
how many different ways are there to seat 4 people around a circular table ,where two sittings are considered the same when each person has same left and right neighbour?Combinatoryhttp://gateoverflow.in/144877/rosen-example-20Thu, 17 Aug 2017 09:06:46 +0000Relation doubt
http://gateoverflow.in/144870/relation-doubt
What is the total number of asymmetric and transitive relation from set a to itself which has n element ?Mathematical Logichttp://gateoverflow.in/144870/relation-doubtThu, 17 Aug 2017 08:53:28 +0000how to draw this graph plz explain in detail
http://gateoverflow.in/144686/how-to-draw-this-graph-plz-explain-in-detail
y = | x^2- 2 | how to draw graph of such equationMathematical Logichttp://gateoverflow.in/144686/how-to-draw-this-graph-plz-explain-in-detailWed, 16 Aug 2017 16:09:01 +0000check this ? is graph correct ? how to find other points
http://gateoverflow.in/144509/check-this-is-graph-correct-how-to-find-other-points
<p><img alt="" src="http://gateoverflow.in/?qa=blob&qa_blobid=1350301987973177666"></p>Mathematical Logichttp://gateoverflow.in/144509/check-this-is-graph-correct-how-to-find-other-pointsWed, 16 Aug 2017 07:24:35 +0000Kenneth Rosen 7th edition Propositional Logic Ex. 1.2 question 38
http://gateoverflow.in/144353/kenneth-rosen-7th-edition-propositional-logic-ex-question
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 colours. The men have different pets and have different favourite drinks. Determine who owns a zebra and whose favourite drink is mineral water (which is one of the favourite drinks) given these clues: The Englishman lives in the red house. The Spaniard owns a dog. The Japanese man is a painter. The Italian drinks tea. The Norwegian lives in the first house on the left. The green house is immediately right of the white one. The photographer breeds snails. The diplomat lives in the yellow house. Milk is drunk in the middle house. The owner of the green house drinks coffee. The Norwegian’s house is next to the blue one. The violinist drinks orange juice. The fox is in a house next to that of the physician. The horse is in a house next to that of the diplomat. [Hint: Make a table where the rows represent the men and columns represent the colour of their houses, their jobs, their pets, and their favourite drinks and use logical reasoning to determine the correct entries in the table.]Mathematical Logichttp://gateoverflow.in/144353/kenneth-rosen-7th-edition-propositional-logic-ex-questionTue, 15 Aug 2017 12:40:08 +0000UPSC prelim test
http://gateoverflow.in/144083/upsc-prelim-test
<p><strong>A bag contains 20 balls. 8 balls are green, 7 are white and 5 are red. What is the minimum number of balls that must be picked up from the bag </strong><strong>blind-folded</strong><strong> (without replacing any of it) to be assured of picking </strong><strong>atleast</strong><strong> one ball of each </strong><strong>colour</strong><strong>?</strong></p>
<p>a) 15 </p>
<p>b) 16</p>
<p>c) 17</p>
<p>d)18</p>Combinatoryhttp://gateoverflow.in/144083/upsc-prelim-testMon, 14 Aug 2017 11:16:58 +0000Mathematical logic
http://gateoverflow.in/143835/mathematical-logic
Let P, Q and R be three atomic propositional assertion. Let X denote (PvQ)$\rightarrow$R and Y denote (P$\rightarrow$R)v(Q$\rightarrow$R). Which of the following is a tautology? <br />
<br />
(A) X$equiv$Y<br />
<br />
(B) X$\rightarrow$Y<br />
<br />
(C) Y$\rightarrow$X<br />
<br />
(D) $\dashv$Y$\rightarrow$ $\dashv$X<br />
<br />
ExplainMathematical Logichttp://gateoverflow.in/143835/mathematical-logicSun, 13 Aug 2017 14:32:09 +0000Rosen_Discrete_Mathematics_and_Its_Applications_7th_Edition/Pg.56/Section 1.4 :predicates and quantifiers/Q.43 and Q.44
http://gateoverflow.in/143763/rosen_discrete_mathematics_and_its_applications_7th_edition
43. Determine whether ∀x(P(x)→Q(x)) and ∀xP (x)→∀xQ(x) are logically equivalent. Justify your answer.<br />
<br />
44. Determine whether ∀x(P(x)↔Q(x)) and ∀ x P (x) ↔ ∀ xQ(x) are logically equivalent. Justify your answer.<br />
<br />
<br />
<br />
First I would like to know , how to proceed with such type of questions and what would be the solution..Mathematical Logichttp://gateoverflow.in/143763/rosen_discrete_mathematics_and_its_applications_7th_editionSun, 13 Aug 2017 08:28:08 +0000ISI KOLKATA 2017
http://gateoverflow.in/143751/isi-kolkata-2017
<h2>Show that if the edge set of a graph G(V,E) with n nodes can be partitioned into 2 trees then there is at least one vertex of degree less than 4 in G.</h2>Graph Theoryhttp://gateoverflow.in/143751/isi-kolkata-2017Sun, 13 Aug 2017 07:28:41 +0000Mathematical logic
http://gateoverflow.in/143744/mathematical-logic
Consider the logical inference :<br />
<br />
I : if it rains then the cricket match will not be played. <br />
<br />
It did not rain<br />
<br />
Inference :the cricket match was played. <br />
<br />
Is the inference I correct? <br />
<br />
ExplainMathematical Logichttp://gateoverflow.in/143744/mathematical-logicSun, 13 Aug 2017 07:05:17 +0000Proposition
http://gateoverflow.in/143687/proposition
X posed many puzzles about an island that has two kinds of inhabitants knights who always tells the truth, and their opposite knaves, who always lie. You encounter two people A and B. What are A and B if A says 'B is a knight' and B says 'two of us are of opposite types'?Mathematical Logichttp://gateoverflow.in/143687/propositionSun, 13 Aug 2017 02:40:53 +0000#combinotirics
http://gateoverflow.in/143639/%23combinotirics
Find the largest integer value of x such that the following inequality holds:<br />
<br />
(10 C x-1) <2*(10 C x)<br />
<br />
In this question if solved line by line i am getting x<6.<br />
<br />
but clearly if you put x=7, it satisfies the inequality and 7 becomes the largest integer. <br />
<br />
Is there a procedure to get answer 7 step by step??Combinatoryhttp://gateoverflow.in/143639/%23combinotiricsSat, 12 Aug 2017 17:39:46 +0000quantifiers
http://gateoverflow.in/143495/quantifiers
In rosen it is given that ∃xp(x) is false when the domain is empty but what about value of ∀xp(x) when the domain is empty ?Mathematical Logichttp://gateoverflow.in/143495/quantifiersSat, 12 Aug 2017 06:56:27 +0000Set Relation
http://gateoverflow.in/143337/set-relation
<p><img alt="" src="http://gateoverflow.in/?qa=blob&qa_blobid=2897476246272035918" style="float:left"></p>
<p> </p>
<p> </p>
<p> </p>
<p> </p>
<p> </p>
<p><img alt="" src="http://gateoverflow.in/?qa=blob&qa_blobid=18400819236796253539" style="float:left"></p>
<p> </p>
<p> </p>
<p> </p>
<p> </p>
<p> </p>
<p> </p>
<p>Answer please explain the ans.</p>
<p>R is antisymmetric then aRb, bRa -> a=b so a-b=0 and 0 is not odd positive then how it is antisymmetric?</p>Set Theory & Algebrahttp://gateoverflow.in/143337/set-relationFri, 11 Aug 2017 16:35:42 +0000graph theory
http://gateoverflow.in/143214/graph-theory
For complete bipartite graph k2,3 , what is the edge connectivity ?Graph Theoryhttp://gateoverflow.in/143214/graph-theoryFri, 11 Aug 2017 07:14:47 +0000Discrete mathematics ex 1.5
http://gateoverflow.in/143198/discrete-mathematics-ex-1-5
How to solve this kind of questions...<br />
<br />
What rules of inference are used in this argument?<br />
<br />
No man is an island<br />
<br />
Manhattan is an island<br />
<br />
Therefore,<br />
<br />
Manhattan is not a man.Mathematical Logichttp://gateoverflow.in/143198/discrete-mathematics-ex-1-5Fri, 11 Aug 2017 06:18:02 +0000equivalence relation: rosen exercise question
http://gateoverflow.in/143177/equivalence-relation-rosen-exercise-question
1- these relations on the set of all functions from Z to Z. Determine the properties they lack for equivalence relation?<br />
<br />
a) {(f, g) | f (0) = g(0) or f (1) = g(1)}<br />
<br />
b) {(f, g) | f (0) = g(1) and f (1) = g(0)}Mathematical Logichttp://gateoverflow.in/143177/equivalence-relation-rosen-exercise-questionFri, 11 Aug 2017 05:27:11 +0000Discrete mathematics
http://gateoverflow.in/143170/discrete-mathematics
Proofs questions are asked in mathematical logic gate?Mathematical Logichttp://gateoverflow.in/143170/discrete-mathematicsFri, 11 Aug 2017 04:23:14 +0000counting
http://gateoverflow.in/143079/counting
<p><img alt="" src="http://gateoverflow.in/?qa=blob&qa_blobid=13048640937689002281"></p>
<p>what does it mean that "each person has same left and right neighbour "?</p>Combinatoryhttp://gateoverflow.in/143079/countingThu, 10 Aug 2017 16:53:03 +0000Discrete mathematics exercise 1.5 6
http://gateoverflow.in/143036/discrete-mathematics-exercise-1-5-6
Use rules of inference to show that the hypothesis<br />
<br />
" If it doesn't rain or it is not foggy, then the sailing race will be held and the lifesaving demonstration will go on ".<br />
<br />
"If the sailing race is held, then the trophy will be awarded"<br />
<br />
"The trophy was not awarded".<br />
<br />
Imply the conclusion "It rained".Mathematical Logichttp://gateoverflow.in/143036/discrete-mathematics-exercise-1-5-6Thu, 10 Aug 2017 14:40:00 +0000General Combinatorics
http://gateoverflow.in/142942/general-combinatorics
<h1>How many 6 digit numbers can be formed from 1, 2, 2, 3, 3, 3, 4, 4, 4, 4, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6?</h1>Combinatoryhttp://gateoverflow.in/142942/general-combinatoricsThu, 10 Aug 2017 07:34:30 +0000J.P TREMBLAY EXCERCISE 1-4.1 4 TH QUESTION
http://gateoverflow.in/142810/j-p-tremblay-excercise-1-4-1-4-th-question
<p><img alt="" src="http://gateoverflow.in/?qa=blob&qa_blobid=12482066827450809867"></p>Mathematical Logichttp://gateoverflow.in/142810/j-p-tremblay-excercise-1-4-1-4-th-questionWed, 09 Aug 2017 16:47:33 +0000Discrete mathematics example 13 Kenneth rosen
http://gateoverflow.in/142589/discrete-mathematics-example-13-kenneth-rosen
<p>How can sentence be translated into a logical expression ?</p>
<p><em><strong>"You can't ride the roller coaster if you are under 4 feet tall unless you are older than 16 years old".</strong></em></p>
<p>Can answer be (!s->r)->!q</p>
<p>Where</p>
<p>q= You can ride the roller coaster</p>
<p>r=You are under 4 feet tall</p>
<p>s= You are older than 16 years old</p>
<p> </p>Mathematical Logichttp://gateoverflow.in/142589/discrete-mathematics-example-13-kenneth-rosenWed, 09 Aug 2017 02:39:08 +0000please solve this Q
http://gateoverflow.in/142533/please-solve-this-q
Q . The maximum number of edges in an undirected graph (simple) with 52 vertices and 3 components areGraph Theoryhttp://gateoverflow.in/142533/please-solve-this-qTue, 08 Aug 2017 18:20:38 +0000probability
http://gateoverflow.in/142502/probability
<p><img alt="" src="http://gateoverflow.in/?qa=blob&qa_blobid=5164991502263664022"></p>Mathematical Logichttp://gateoverflow.in/142502/probabilityTue, 08 Aug 2017 14:49:42 +0000number of paths in a graph
http://gateoverflow.in/142407/number-of-paths-in-a-graph
Find the number of paths of length n between two different vertices in K4 if n is<br />
a) 2. b) 3. c) 4. d) 5.Mathematical Logichttp://gateoverflow.in/142407/number-of-paths-in-a-graphTue, 08 Aug 2017 05:38:07 +0000Limits
http://gateoverflow.in/142404/limits
can you please solve <br />
<br />
lt x->1 x^3-x^2logx+logx-1/x^2-1<br />
<br />
using L-Hospitals ruleMathematical Logichttp://gateoverflow.in/142404/limitsTue, 08 Aug 2017 05:16:59 +0000J P TREMBLAY R MANOHAR EXCERCISE1-2.11
http://gateoverflow.in/142352/j-p-tremblay-r-manohar-excercise1-2-11
P->(Q->P) IS EQUIVALENT TO ~P->(P->Q) WITHOUT USING TRUTH TABLEMathematical Logichttp://gateoverflow.in/142352/j-p-tremblay-r-manohar-excercise1-2-11Mon, 07 Aug 2017 16:39:55 +0000doubt
http://gateoverflow.in/142307/doubt
Given 3 characters a, b, c. Find the number of strings of length n that can be formed from these 3 characters. Given that : we can use ‘a’ as many times as we want, ‘b’ maximum once, and ‘c’ maximum twice.Mathematical Logichttp://gateoverflow.in/142307/doubtMon, 07 Aug 2017 13:29:44 +0000hey can i do this is it allowed , and if not then someone plz solve it
http://gateoverflow.in/142106/hey-can-do-this-is-it-allowed-and-if-not-then-someone-plz-solve
<p><img alt="" src="http://gateoverflow.in/?qa=blob&qa_blobid=2555709503946725421"></p>Mathematical Logichttp://gateoverflow.in/142106/hey-can-do-this-is-it-allowed-and-if-not-then-someone-plz-solveSun, 06 Aug 2017 14:03:21 +0000Relations
http://gateoverflow.in/142068/relations
Consider the set {2,3,4} and define partial ordering if a divides b.<br />
<br />
Now element 3 is maximal or minimal.Set Theory & Algebrahttp://gateoverflow.in/142068/relationsSun, 06 Aug 2017 11:28:44 +0000Discrete Maths Kenneth Rosen Nested Quantifiers Ex 1.5 Q8
http://gateoverflow.in/141969/discrete-maths-kenneth-rosen-nested-quantifiers-ex-1-5-q8
<p><em>Let Q(x, y) be the statement “student x has been a contestant
<br>
on quiz show y.” Express each of these sentences
<br>
in terms of Q(x, y), quantifiers, and logical connectives,
<br>
where the domain for x consists of all students at your
<br>
school and for y consists of all quiz shows on television</em>.</p>
<p>
<br>
a) There is a student at your school who has been a contestant
<br>
on a television quiz show.
<br>
b) No student at your school has ever been a contestant
<br>
on a television quiz show.
<br>
c) There is a student at your school who has been a contestant
<br>
on Jeopardy and on Wheel of Fortune.
<br>
d) Every television quiz show has had a student from
<br>
your school as a contestant.
<br>
e) At least two students from your school have been contestants
<br>
on Jeopardy.</p>Mathematical Logichttp://gateoverflow.in/141969/discrete-maths-kenneth-rosen-nested-quantifiers-ex-1-5-q8Sat, 05 Aug 2017 19:07:12 +0000Sheldon Ross - Probability (2nd chapter)
http://gateoverflow.in/141823/sheldon-ross-probability-2nd-chapter
<p>Poker dice is played by simultaneously rolling 5 dice.Show that</p>
<p>(a) P{no two alike} = .0926;
<br>
(b) P{one pair} = .4630;
<br>
(c) P{two pair} = .2315;
<br>
(d) P{three alike} = .1543;
<br>
(e) P{full house} = .0386;
<br>
(f) P{four alike} = .0193;
<br>
(g) P{five alike} = .0008.</p>
<p><span class="marker">My doubt is how is this different from poker played by cards? Is it that when we play via dice the order of the dice outcome matters which doesn't in case of cards.(i.e the order of cards in hand). So if we think the case of having one pair as </span></p>
<p><span class="marker"><6 6 5 1 2> and <6 5 1 2 6> both outcomes are different?</span></p>
<p><span class="marker">but <6(1st six) 5 1 2 6 (second six)> and <6(2nd six) 5 1 2 6(1st six)> both are same,since its the same one pair but the pairs doesn't generate new outcome when position is changed.</span></p>
<p>i.e for question (b) probability is = 6C1 (for selecting pair outcome) * 5C2 (possibility of selecting a pair of hand out of five,but order does not matter when pair partners are exchanged) * 5 * 4* 3 (because order matters of the outcomes of other non-pairs) this total divided by 6^5. Is my assumption true?</p>Combinatoryhttp://gateoverflow.in/141823/sheldon-ross-probability-2nd-chapterSat, 05 Aug 2017 07:41:33 +0000