GATE Overflow - Recent questions tagged discrete-mathematics
http://gateoverflow.in/tag/discrete-mathematics
Powered by Question2AnswerGROUP THEORY
http://gateoverflow.in/105538/group-theory
Can someone tell whether these topics are important in GROUP THEORY?<br />
<br />
ISOMORPHIC GROUPS<br />
<br />
NORMAL GROUPS<br />
<br />
COSETS.Set Theory & Algebrahttp://gateoverflow.in/105538/group-theorySat, 14 Jan 2017 15:46:36 +0000Maths: Probability Distribution Que01
http://gateoverflow.in/104418/maths-probability-distribution-que01
<p><img alt="" src="http://gateoverflow.in/?qa=blob&qa_blobid=15533185615533012495"></p>Probabilityhttp://gateoverflow.in/104418/maths-probability-distribution-que01Thu, 12 Jan 2017 08:14:34 +0000Graph Theory
http://gateoverflow.in/104390/graph-theory
<p><img alt="" src="http://gateoverflow.in/?qa=blob&qa_blobid=8422524080339804649"></p>Programminghttp://gateoverflow.in/104390/graph-theoryThu, 12 Jan 2017 07:32:32 +0000Maths: Group Theorey
http://gateoverflow.in/104241/maths-group-theorey
<p>A group G in which (ab)<sup>2</sup> = a<sup>2</sup>b<sup>2</sup> for all a,b in G is neccessarily</p>
<p>A. finite
<br>
B. cyclic
<br>
C. of order two
<br>
D. Abelian</p>
<p>please prove it
<br>
ands: D </p>Set Theory & Algebrahttp://gateoverflow.in/104241/maths-group-theoreyWed, 11 Jan 2017 19:47:06 +0000Maths: Group Theorey
http://gateoverflow.in/104236/maths-group-theorey
<p>Let * be the binary operation on the rational number given by a*b=a+b+2ab. which of the following are true?
<br>
i. * is commutative
<br>
ii. there is a rational number that is an identity with * operation
<br>
iii. every rational numebr has an inverse with * operation</p>
<p><span class="marker">I know that i is true and iii is false but why is ii false?</span>
<br>
<br>
Ans: (i) is only true</p>Set Theory & Algebrahttp://gateoverflow.in/104236/maths-group-theoreyWed, 11 Jan 2017 19:34:06 +0000#Chromatic number , Planarity
http://gateoverflow.in/104130/%23chromatic-number-planarity
Let G be a planar graph such that every face is bordered by exactly 3 edges.Which of the following can never be the value for χ(G) ? (where χ(G) is the chromatic number of G)<br />
<br />
a) 2<br />
<br />
b) 3<br />
<br />
c) 4<br />
<br />
d) None of these<br />
<br />
PS : (Explain: "every face is bordered by exactly 3 edges. ")Graph Theoryhttp://gateoverflow.in/104130/%23chromatic-number-planarityWed, 11 Jan 2017 15:09:19 +0000GATE FORUM
http://gateoverflow.in/103201/gate-forum
<p><img alt="" height="77" src="http://gateoverflow.in/?qa=blob&qa_blobid=5026250597681756319" width="667"></p>
<p>Shouldn't it be 6?</p>Mathematical Logichttp://gateoverflow.in/103201/gate-forumMon, 09 Jan 2017 14:30:16 +0000doubt
http://gateoverflow.in/102767/doubt
<p><img alt="" src="http://gateoverflow.in/?qa=blob&qa_blobid=14244852771150034296"></p>Mathematical Logichttp://gateoverflow.in/102767/doubtSun, 08 Jan 2017 15:40:49 +0000maths
http://gateoverflow.in/101844/maths
<p>When the curves, y = log<sub>10</sub>x and y = x<sup>–1</sup> are drawn in x – y plane. The number of times they intersect for values x ≥ 1 is ________.</p>Mathematical Logichttp://gateoverflow.in/101844/mathsSat, 07 Jan 2017 02:35:46 +0000Relations and Combinatorics
http://gateoverflow.in/101502/relations-and-combinatorics
$\begin{align*} &S = \left \{ G_i \;\; | \; G_i \in \text{ lebeled trees with 4 vertices} \right \} \\ &\text{Relation } \quad R = \left \{ {\color{red}{\left ( G_i,G_j \right )}} \; | G_i,G_j \in S \;\; \text{and} \;\; G_i,G_j \;\; \text{are} \;\; \text{isomorphic to each other} \right \} \end{align*}$<br />
<br />
No of equivalent classes of $R$ ?Combinatoryhttp://gateoverflow.in/101502/relations-and-combinatoricsFri, 06 Jan 2017 10:47:34 +0000Rosen-Counting
http://gateoverflow.in/101340/rosen-counting
Once a computerworm infects a personal computer via an<br />
infected e-mail message, it sends a copy of itself to 100 email<br />
addresses it finds in the electronic message mailbox<br />
on this personal computer. What is the maximum number<br />
of different computers this one computer can infect in the<br />
time it takes for the infected message to be forwarded five<br />
times?<br />
<br />
I wanted to verify this answer and method,there is no answer given for this question.Combinatoryhttp://gateoverflow.in/101340/rosen-countingFri, 06 Jan 2017 05:24:03 +0000discrete
http://gateoverflow.in/101182/discrete
<p>find the solution of the recurence relation</p>
<p>a<sub>n </sub>=3a<sub>n-1</sub> + 2n initial conditon is given as a<sub>1</sub>=3 ?</p>Mathematical Logichttp://gateoverflow.in/101182/discreteThu, 05 Jan 2017 16:30:38 +0000graph theory
http://gateoverflow.in/100206/graph-theory
Assumed undirected graph G is connected. G has 6vertices and 10 edges. Find<br />
the minimum number of edges whose deletion from graph G is always guarantee<br />
that it will become disconnected.Graph Theoryhttp://gateoverflow.in/100206/graph-theoryTue, 03 Jan 2017 20:57:09 +0000Maths: Graph Theory
http://gateoverflow.in/99639/maths-graph-theory
<p>Let G be a graph with 10 vertices and 31 edges. If G has 3 vertices of degree 10, 1 vertex of degree 8 and 2 vertices of degree 5 and the other four vertices of degree at least 3, how many vertices are of degree 3________?</p>
<p>my solution:
<br>
<br>
Σ deg(v) = 2|E|</p>
<p>3*10 + 1*8 + 2*5 + 4*(>=3) = 2*31
<br>
<br>
4*(>=3) = 62- (30+8+10) = 14
<br>
<br>
I think we can have 3 vertices each of degree 3 and vertex of degree 5, so my answer is 3 but given answer is 2.
<br>
<br>
<span class="marker">Given answer: 2</span></p>Graph Theoryhttp://gateoverflow.in/99639/maths-graph-theoryMon, 02 Jan 2017 16:12:18 +0000Maths: Counting Relations
http://gateoverflow.in/99470/maths-counting-relations
<p>Let A = {1,2,3,4}. since each element of P(AxA) is subset of AxA, it is binary relation on A
<br>
Assuming each relation in P(AxA) is equally likely to be chosen,
<br>
<br>
i. what is the probability that a randomly chosen relation is reflexive
<br>
a. 1/2<sup>6</sup>
<br>
b. 1/2<sup>4</sup>
<br>
c. 1/2<sup>6</sup>
<br>
d. 1/2<sup>12</sup>
<br>
<span class="marker">Given Ans: 1/2<sup>4</sup></span>
<br>
ii what is the probability that a randomly chosen relation is Symmetric
<br>
a. 1/2<sup>16</sup>
<br>
b. 1/2<sup>4</sup>
<br>
c. 1/2<sup>6</sup>
<br>
d. 1/2<sup>12</sup>
<br>
<span class="marker">Given Ans: 1/2<sup>6</sup></span></p>Set Theory & Algebrahttp://gateoverflow.in/99470/maths-counting-relationsMon, 02 Jan 2017 09:54:13 +0000Maths: GroupTheory
http://gateoverflow.in/99461/maths-grouptheory
Let S = R - {-1} and define a binary operation on S by a*b = a+b+ab, what is true about (S,*)<br />
A. (S,*) is a group but is not commutative<br />
B. (S,*) is a group and is also commutative<br />
C. (S,*) is not a group because inverse of 1 doesn't exist<br />
<br />
"How to check if inverse and identity element exist?Set Theory & Algebrahttp://gateoverflow.in/99461/maths-grouptheoryMon, 02 Jan 2017 09:27:35 +0000Maths: Lattice
http://gateoverflow.in/99370/maths-lattice
<p><img alt="" src="http://gateoverflow.in/?qa=blob&qa_blobid=13794931896604016917"></p>
<p>A. Not a Lattice
<br>
B. Lattice but not a complemented Lattice
<br>
C. A complemented Lattice
<br>
D. A Boolean Algebra</p>Set Theory & Algebrahttp://gateoverflow.in/99370/maths-latticeMon, 02 Jan 2017 06:05:34 +0000Maths: functions
http://gateoverflow.in/99368/maths-functions
<p>Given function $f(x)=log\frac{1+x}{1-x} and g(x)=\frac{3x+x^{2}}{1+3x^{2}}$ then (fog)(x)</p>
<p>1. -f(x)
<br>
2. f(x)
<br>
3. [f(x)]<sup>3</sup>
<br>
<sup>4. None of these</sup></p>Set Theory & Algebrahttp://gateoverflow.in/99368/maths-functionsMon, 02 Jan 2017 06:01:08 +0000Maths: Functions
http://gateoverflow.in/99351/maths-functions
<p>if $f(x)=\frac{x-1}{x+1}$ , x∈R-{-1}, then f<sup>-1</sup>(x) is equal to</p>
<p> </p>
<p>$a. \frac{x-1}{x+1} b.\frac{x+1}{x-1} c.\frac{2}{1+x}$ d.Does Not exist</p>Graph Theoryhttp://gateoverflow.in/99351/maths-functionsMon, 02 Jan 2017 05:41:33 +0000Maths: Set Theory
http://gateoverflow.in/99348/maths-set-theory
The Set (A U B U C) ∩ (A ∩ B' ∩ C')' ∩ C' is equal to<br />
1. B ∩ C'<br />
2. A ∩ C<br />
3. B' ∩ C'<br />
4. None of theseSet Theory & Algebrahttp://gateoverflow.in/99348/maths-set-theoryMon, 02 Jan 2017 05:36:03 +0000Maths: Relations
http://gateoverflow.in/99345/maths-relations
<p>An Equivalence relation R on Z defined by <sub>a</sub>R<sub>b </sub>if 5a=2b(mod3). which of the following is an equivalence class of R?
<br>
1. The Set {x ∈ Z: x=3y for some y∈Z}
<br>
2. The even integers
<br>
3. The odd integers
<br>
4. the set {x<sup>2 </sup>: x ∈ Z}</p>Set Theory & Algebrahttp://gateoverflow.in/99345/maths-relationsMon, 02 Jan 2017 05:30:07 +0000Maths: relations
http://gateoverflow.in/99343/maths-relations
<p>Which of the following is not a relation on R?
<br>
(A) A subset of R containg 2 real numbers
<br>
(B) A set containing a single point (a,b) where both a and b are integers
<br>
(C) the set {(r,s) ∈ RxR : r< s}
<br>
(D) The set {(a,b) ∈ RxR: a<sup>2 </sup>+ b<sup><span style="font-size:10.8333px">3</span></sup><span style="font-size:10.8333px">=1</span>}</p>Set Theory & Algebrahttp://gateoverflow.in/99343/maths-relationsMon, 02 Jan 2017 05:24:39 +0000Maths: Group Theory
http://gateoverflow.in/99342/maths-group-theory
<p>Consider the following binary operations on Z. which of the following operations form a group
<br>
i. x*y = x+y+2 for x,y ∈ Z.
<br>
ii. x*y = xy + 2x + 2y +2 for x,y ∈ Z
<br>
iii. x*y=x<sup>2</sup>y<sup>2 </sup>for x,y ∈ Z</p>Set Theory & Algebrahttp://gateoverflow.in/99342/maths-group-theoryMon, 02 Jan 2017 05:19:54 +0000Counting
http://gateoverflow.in/99333/counting
How many eight digit numbers are there, that contain a 5 and a 6____________? please explain!<br />
<br />
Ans: 8486912Combinatoryhttp://gateoverflow.in/99333/countingMon, 02 Jan 2017 05:01:11 +0000TheTrevTutor discrete maths 2 videos
http://gateoverflow.in/98563/thetrevtutor-discrete-maths-2-videos
<p>I want to know how good are the videos of discrete maths by TheTrevTutor. Has anyone been following the videos while preparing for GATE? </p>
<p> </p>
<p><a rel="nofollow" href="https://www.youtube.com/watch?v=DBugSTeX1zw&list=PLDDGPdw7e6Aj0amDsYInT_8p6xTSTGEi2">https://www.youtube.com/watch?v=DBugSTeX1zw&list=PLDDGPdw7e6Aj0amDsYInT_8p6xTSTGEi2</a></p>Combinatoryhttp://gateoverflow.in/98563/thetrevtutor-discrete-maths-2-videosFri, 30 Dec 2016 19:11:02 +0000Combinatorics
http://gateoverflow.in/98131/combinatorics
<p><img alt="" src="http://gateoverflow.in/?qa=blob&qa_blobid=14734480078273353524"></p>
<p>The answer given is<strong> <sup>n-k+1</sup>C<sub>2 </sub></strong>but couldn't understand how both are related</p>Combinatoryhttp://gateoverflow.in/98131/combinatoricsThu, 29 Dec 2016 13:03:07 +0000Number of Solutions for the quation
http://gateoverflow.in/98038/number-of-solutions-for-the-quation
How many integral solutions exist for the system of equations x+y+z =15 where 0<=x,y,z<=10 ?<br />
<br />
Ans given is 620. I am getting 91<br />
<br />
Could someone point out the flaw in the below logic?<br />
<br />
Mehod Used : There are 10 stars and 3 bins with multi choose 17C2 = 136<br />
<br />
Invalid Solutions (Any of them assigned >=11 ) 3C1 * N( x+y+z = 4) => 3*6C2 = 15 *3 =45 <br />
<br />
136-45=91Combinatoryhttp://gateoverflow.in/98038/number-of-solutions-for-the-quationThu, 29 Dec 2016 07:13:41 +0000[Rosen Textbook Problem] Complementary Graph
http://gateoverflow.in/97560/rosen-textbook-problem-complementary-graph
The complementary graph G' of a simple graph G has the same vertices as G. Two vertices are adjacent in G' if and only if they are not adjacent in G. Define Qn' (Hypercube complement).<br />
<br />
Answer given :-The graph whose vertices are bit strings of length n and two vertices are adjacent if the bit string represented by them differe by more than one bit.<br />
<br />
I want to understand that whether the complement graph will have self loops?Because the answer given doesn't consider self loops.I mean why are we not considering the bit strings that are differing by 0 bit,as these are also not there in original graph ,so it must be in complementary graph?Graph Theoryhttp://gateoverflow.in/97560/rosen-textbook-problem-complementary-graphTue, 27 Dec 2016 23:53:29 +0000Kenneth Rosen (Special Indian Edition) Section 6.1 Exercise Problem #9d
http://gateoverflow.in/95581/kenneth-rosen-special-indian-edition-section-exercise-problem
Solve the recurrence relation $a_n = a_{n-1} + 2n + 3, a_0 = 4$Combinatoryhttp://gateoverflow.in/95581/kenneth-rosen-special-indian-edition-section-exercise-problemThu, 22 Dec 2016 17:22:54 +0000Rosen Exercise problem
http://gateoverflow.in/94656/rosen-exercise-problem
1. What is good for corporations is good for the United States.<br />
<br />
2. What is good for the United States is good for you.<br />
<br />
3. What is good for the corporations is for you to buy lots of stuffs<br />
<br />
<br />
<br />
What are the valid conclusions? Please explain the solutionMathematical Logichttp://gateoverflow.in/94656/rosen-exercise-problemTue, 20 Dec 2016 05:39:40 +0000Kenneth Rosen (Special Indian Edition) Section 5.1 Exercise Problem # 5
http://gateoverflow.in/94477/kenneth-rosen-special-indian-edition-section-exercise-problem
<p><strong>Question</strong>: Six different airlines fly from New York to Denver and seven fly from Denver to San Francisco. How many different pairs of airlines can you choose on which to book a trip from New York to San Francisco via Denver, when you pick an airline for the flight to Denver and an airline for the continuation flight to San Francisco ? How many of these pairs involve more than one airline ?</p>
<p> </p>Combinatoryhttp://gateoverflow.in/94477/kenneth-rosen-special-indian-edition-section-exercise-problemMon, 19 Dec 2016 14:23:26 +0000Counting
http://gateoverflow.in/94382/counting
How many ways you can put 3 identical balls into 2 box so that each box has at-most 2 balls?<br />
<br />
Is the answer 2?Combinatoryhttp://gateoverflow.in/94382/countingMon, 19 Dec 2016 08:18:25 +0000Counting
http://gateoverflow.in/94304/counting
How many ways, can sum be equal to 12 of 3 dice?<br />
<br />
Solution:<br />
x1+x2+x3=12 <br />
where 1<=x1<=6;1<=x2<=6; 1<=x3<=6<br />
How to solve it further?Combinatoryhttp://gateoverflow.in/94304/countingMon, 19 Dec 2016 05:58:36 +0000Relation
http://gateoverflow.in/92673/relation
<p>Which of the following is/are true ?</p>
<ul>
<li>A. $\text{R}$ is a reflexive relation on a set $\text{A}$, then $\text{R}^{n}$ is reflexive for all $n\geq0$</li>
<li>B. Relation $\text{R}$ on set $A$ is reflexive if and only if inverse relation $R^{-1}$ is reflexive.</li>
<li>C Relation $\text{R}$ on set $A$ is antisymmetric if and only $R \cap R^{-1}$ is a subest of diagonal relation $\Delta = \left \{ (a,a) \; | a \in A \right \}$</li>
<li>D. $M_{S\circ R} = M_R \; \odot M_S$ where $\odot$ is boolean product.</li>
</ul>Set Theory & Algebrahttp://gateoverflow.in/92673/relationWed, 14 Dec 2016 13:00:03 +0000Relation composition
http://gateoverflow.in/92672/relation-composition
$R$ and $S$ are two relations on a set $A$<br />
<br />
$$\begin{align*} M_R = \begin{bmatrix} 1 & 0 & 1 \\ 1 & 0 & 0 \\ 0 & 1 & 0 \\ \end{bmatrix} \qquad M_S = \begin{bmatrix} 0 & 1 & 1 \\ 0 & 1 & 0 \\ 1 & 1 & 0 \\ \end{bmatrix} \end{align*}$$<br />
<br />
Then matrices for $R \cap S$ and $R \cup S$ ?Set Theory & Algebrahttp://gateoverflow.in/92672/relation-compositionWed, 14 Dec 2016 13:00:00 +0000Relation
http://gateoverflow.in/92671/relation
<p>How many non zero entries does the matrix representing relation $R$ on a set $A$ = $\left \{ 1,2,3,4,5,6....1000 \right \}$.</p>
<ul>
<li>a. $R = \left \{ (x,y) \; | x = y \pm 1 \right \}$</li>
<li>b. $R = \left \{ (x,y) \; | x + y = 1000 \right \}$</li>
</ul>Set Theory & Algebrahttp://gateoverflow.in/92671/relationWed, 14 Dec 2016 12:59:52 +0000Graph theory
http://gateoverflow.in/92030/graph-theory
proof :- A connected graph any two paths of maximum length share at least one vertexGraph Theoryhttp://gateoverflow.in/92030/graph-theoryMon, 12 Dec 2016 10:39:47 +0000binomial theorem and expansions
http://gateoverflow.in/91878/binomial-theorem-and-expansions
<p>can anyone please explain these things:</p>
<p>formula for (1-x)<sup>n</sup></p>
<p>formula for 1/(1-x)<sup>n</sup></p>
<p>general term in expansion of (1-x)<sup>n </sup>and 1/(1-x)<sup>n</sup></p>
<p>and coeffecient of a term in these expansions.</p>
<p>please elaborate a little because i have read few questions on generating functions and binomial where these things are used but i am getting very confused.i dun know much about them and gathering info from internet is also confusing me.</p>Combinatoryhttp://gateoverflow.in/91878/binomial-theorem-and-expansionsSun, 11 Dec 2016 20:23:48 +0000counting
http://gateoverflow.in/91481/counting
how many number are possible of 4 digits whose sum is 12.Combinatoryhttp://gateoverflow.in/91481/countingSat, 10 Dec 2016 15:58:58 +0000self made
http://gateoverflow.in/89250/self-made
<blockquote>
<p>Anyone plz help in differentiating "consistency, inconsistency, valid,invalid,tautology, contradiction,arguments,fallacy" ?</p>
</blockquote>
<p> </p>Mathematical Logichttp://gateoverflow.in/89250/self-madeSun, 04 Dec 2016 07:25:26 +0000GATEBOOK
http://gateoverflow.in/85030/gatebook
There are 5 bins labelled 1,2,3,4,5. Now there are 5 numbers 1,2,3,4,5. How many combinations exist such that 1,2,3 all arent at proper place?<br />
<br />
Now, we can easily solve using inclusion-exclusion principle.<br />
<br />
But, sometimes this principle counts duplicates(Kenneth Rosen has one problem in which diagram in the form of tree is shown). So, most of the times, I try to solve using recurrance relation which always gives correct answers.<br />
<br />
This is the first problem where I am not able to set up a recurrance relation. Could anyone help?Combinatoryhttp://gateoverflow.in/85030/gatebookWed, 23 Nov 2016 05:36:30 +0000graph theory
http://gateoverflow.in/84795/graph-theory
Which of the following statements is/are TRUE?<br />
[P] Every disconnected graph has an isolated vertex<br />
[Q] A graph is connected if and only if some vertex is connected to all other vertices<br />
[R] The edge set of every closed trail can be partitioned into edge sets of cycles<br />
[S] If a maximal trail in a graph is not closed, then its endpoints have odd degreeGraph Theoryhttp://gateoverflow.in/84795/graph-theoryTue, 22 Nov 2016 07:25:21 +0000GATE1987-2d
http://gateoverflow.in/80583/gate1987-2d
State whether the following statements are TRUE or FALSE:<br />
<br />
The union of two equivalence relations is also an equivalence relation.Set Theory & Algebrahttp://gateoverflow.in/80583/gate1987-2dWed, 09 Nov 2016 13:10:45 +0000Doubt: Graph Theory
http://gateoverflow.in/80069/doubt-graph-theory
When say that with n vertices there are total 2^(n(n-1)/2) connected/disconnected graph possible, in this case we are assuming that vertices are labelled, right??<br />
<br />
<br />
<br />
Is there any formula to count number of connected/disconnected graphs possible with n unlabeled vertices?Graph Theoryhttp://gateoverflow.in/80069/doubt-graph-theoryTue, 08 Nov 2016 03:11:14 +0000Doubt: Propositional Logic Que02
http://gateoverflow.in/79519/doubt-propositional-logic-que02
Consider the following WFFs<br />
1. ∀x purple(x) Λ Mushroom(x) → Poisinonous(x)<br />
2. ∀x purple(x) → Mushroom(x) → Poisinonous(x)<br />
3. Mushroom(x) → ∀x purple(x) → Poisinonous(x)<br />
How many statements are equivalent?<br />
<br />
My Doubts:<br />
1. statement 2 and 3 are equivalent but how statement 1 is equivalent to 2&3.<br />
2. Does ∀x has scope for all three propostional functions or just for purple(x)Mathematical Logichttp://gateoverflow.in/79519/doubt-propositional-logic-que02Sun, 06 Nov 2016 13:26:11 +0000Doubt: Propositional Logic: Que 01
http://gateoverflow.in/79505/doubt-propositional-logic-que-01
<p>This is the given solution:
<br>
<img alt="" src="http://gateoverflow.in/?qa=blob&qa_blobid=6882825661556739814"></p>
<p>If I only need to compute " There exists a women who likes a man who doesn't like all vegetarians" then i will remove NOT from the given expression and it will be as:
<br>
<img alt="" src="http://gateoverflow.in/?qa=blob&qa_blobid=16714539983205302590"></p>
<p>my question, where is "ALL Vegetarian" taken care? please explain?
<br>
</p>Mathematical Logichttp://gateoverflow.in/79505/doubt-propositional-logic-que-01Sun, 06 Nov 2016 12:54:39 +0000Doubt: Propositional Logic
http://gateoverflow.in/79481/doubt-propositional-logic
The WFF( Well Formed Formula) representing the sentence "if everybody respects somebody, then that person is a king" is<br />
Note: Respect(T1,T2) means, T1 respects T2<br />
<br />
Answer: ∀x(∀y(person(y) --> respect(y,x))-->King(x)<br />
<br />
Why did we use Universal Quanitifier ∀ for x, it should be ∃x, because everyone can't be a king.Mathematical Logichttp://gateoverflow.in/79481/doubt-propositional-logicSun, 06 Nov 2016 11:57:15 +0000DM: Duality
http://gateoverflow.in/79450/dm-duality
<p>If A* represents the dual of A, if a logical equivalence is true then its dual is also true (A<->B then A*<->B*)</p>
<p><span style="line-height:1.6">Is this above statement true?</span></p>Mathematical Logichttp://gateoverflow.in/79450/dm-dualitySun, 06 Nov 2016 09:29:12 +0000Made Easy Test
http://gateoverflow.in/78204/made-easy-test
<p><img alt="" src="http://gateoverflow.in/?qa=blob&qa_blobid=16443538790148249044"></p>Set Theory & Algebrahttp://gateoverflow.in/78204/made-easy-testWed, 02 Nov 2016 06:12:49 +0000Made-Easy | how many chits will go into the same box ?
http://gateoverflow.in/78071/made-easy-how-many-chits-will-go-into-the-same-box
A community of 5 members is to be formed out of 10 people. The names are written in chits of paper and put into 6 boxes. So how many chits will go into the same box?<br />
<br />
<br />
<br />
Anyone, please make me understand this question.Combinatoryhttp://gateoverflow.in/78071/made-easy-how-many-chits-will-go-into-the-same-boxTue, 01 Nov 2016 12:46:51 +0000