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Powered by Question2Answerrosen-prepositional logic - excercise 1.2 16
http://gateoverflow.in/130668/rosen-prepositional-logic-excercise-1-2-16
<p>An explorer is captured by a group of cannibals. There are</p>
<p>two types of cannibals—those who always tell the truth</p>
<p>and those who always lie. The cannibals will barbecue</p>
<p>the explorer unless he can determine whether a particular</p>
<p>cannibal always lies or always tells the truth. He is</p>
<p>allowed to ask the cannibal exactly one question..</p>
<p> </p>
<p><strong>a) </strong>Explain why the question “Are you a liar?” does not</p>
<p>work.</p>
<p><strong>b) </strong>Find a question that the explorer can use to determine</p>
<p>whether the cannibal always lies or always tells the</p>
<p>truth.</p>
<p>in the below link, it mentioned double negation will work. I am not getting what is double negation here. ow the cannibal will consider as two separate question.</p>
<p><a rel="nofollow" href="https://math.stackexchange.com/questions/1078866/is-this-a-correct-solution-to-determining-which-of-two-people-is-the-liar-using">https://math.stackexchange.com/questions/1078866/is-this-a-correct-solution-to-determining-which-of-two-people-is-the-liar-using</a></p>Mathematical Logichttp://gateoverflow.in/130668/rosen-prepositional-logic-excercise-1-2-16Wed, 24 May 2017 11:01:11 +0000Rosen-Prepositional Logic - Excercise 1.2
http://gateoverflow.in/130605/rosen-prepositional-logic-excercise-1-2
<p>You cannot edit a protected Wikipedia entry unless you</p>
<p>are an administrator. Express your answer in terms of <em>e</em>:</p>
<p>“You can edit a protected Wikipedia entry” and <em>a</em>: “You</p>
<p>are an administrator.”
<br>
<br>
the answer given is e----> a</p>
<p>This question seems to be silly. But I am getting so much confused. why can't the answer be a--->e.
<br>
If the user is an Administrator, he can edit the wikipedia entry.
<br>
<br>
please clarify.</p>Mathematical Logichttp://gateoverflow.in/130605/rosen-prepositional-logic-excercise-1-2Wed, 24 May 2017 06:29:11 +0000Null Qunatification Rule
http://gateoverflow.in/130504/null-qunatification-rule
<p>What is the meaning of <strong>NULL Quantification Rule</strong> in Predicate Calculus ?</p>Mathematical Logichttp://gateoverflow.in/130504/null-qunatification-ruleTue, 23 May 2017 03:57:15 +0000Rosen Exercise
http://gateoverflow.in/130422/rosen-exercise
Let S(x) be the predicate “x is a student,” F(x) the predicate<br />
“x is a faculty member,” and A(x, y) the predicate<br />
“x has asked y a question,” where the domain consists of<br />
all people associated with your school.<br />
<br />
Express the following sentence using quantifiers:<br />
<br />
Some student has asked every faculty member a question.Mathematical Logichttp://gateoverflow.in/130422/rosen-exerciseMon, 22 May 2017 10:38:36 +0000rosen ex 1.3 q-37
http://gateoverflow.in/130367/rosen-ex-1-3-q-37
c) A student must take at least 60 course hours, or at least 45 course hours and write master's thesis, and receive a grade no lower than a B in all required courses, to receive a master's degree.<br />
<br />
<br />
<br />
My question :<br />
<br />
In book answer is given as MD(x)->{set of conditions}<br />
<br />
And my answer is {Set of conditions}->MD(x)<br />
<br />
As we know a->b ≠ b->a<br />
<br />
Why anyone of the above is correct. ?Mathematical Logichttp://gateoverflow.in/130367/rosen-ex-1-3-q-37Mon, 22 May 2017 02:22:54 +0000Gate 2015
http://gateoverflow.in/130337/gate-2015
Out of the following high of the battery achieved highest growthMathematical Logichttp://gateoverflow.in/130337/gate-2015Sun, 21 May 2017 14:07:29 +0000ME Gate, 2014
http://gateoverflow.in/130320/me-gate-2014
<p><a rel="nofollow" href="https://www.facebook.com/photo.php?fbid=125621908008187&set=gm.635960336609180&type=3&theater">https://www.facebook.com/photo.php?fbid=125621908008187&set=gm.635960336609180&type=3&theater</a>
<br>
plz solve this</p>Mathematical Logichttp://gateoverflow.in/130320/me-gate-2014Sun, 21 May 2017 09:51:48 +0000graphtheory,Narsingh Deo,4.26
http://gateoverflow.in/130286/graphtheory-narsingh-deo-4-26
Suppose a single tennis tournament is arranged among n players and the number of matches planned is a fixed number e (where n-1 < e < n(n-1)/2 ).For sake of fairness,how will you make sure that some players do not group together and isolate an individual (or a group of players).Graph Theoryhttp://gateoverflow.in/130286/graphtheory-narsingh-deo-4-26Sun, 21 May 2017 03:34:20 +0000#Graphtheory
http://gateoverflow.in/130285/%23graphtheory
Construct a graph G with edge connectivity of G =4 ,vertex connectivity of G =3 and degree of every vertex of G >=5Graph Theoryhttp://gateoverflow.in/130285/%23graphtheorySun, 21 May 2017 02:56:10 +0000$a_n = 4^n + 6^n$
http://gateoverflow.in/130200/%24a_n-4-n-6-n%24
If $a_n = 4^n + 6^n$ Find the value of $a_{40} \text { mod } 25$Set Theory & Algebrahttp://gateoverflow.in/130200/%24a_n-4-n-6-n%24Fri, 19 May 2017 19:52:44 +00002 - connected graph
http://gateoverflow.in/130141/2-connected-graph
<p>For a <strong>regular graph</strong> how much large the value of degree (for each vertices) should be such that the graph is $2$ - connected. (vertex wise).</p>
<p>I did in this way :</p>
<p>$\begin{align*} &\quad \kappa(G) \leq \frac{2\cdot e}{n} \qquad \text{ where } \kappa(G) = \text{ vertex connectivity } \\ &\Rightarrow 2 \leq \frac{2\cdot e}{n} \\ &\Rightarrow n \leq e \\ &\Rightarrow n \leq \frac{\sum \left ( d_i \right )}{2} \\ &\Rightarrow n \leq \frac{n \cdot d}{2} \\ &\Rightarrow d \geq 2 \\ \end{align*}$</p>
<p>The above case can be realized by thinking of a <strong>cycle graph</strong> of $n$ vertices.</p>
<p>But in the following case :</p>
<p><img alt="" src="http://gateoverflow.in/?qa=blob&qa_blobid=15360590681287688332"></p>
<p>This graph is 3 regular and not 2- connected although $d \geq 2$ is satisfied.</p>
<p>Why this $d \geq 2$ is trivial and not working in some cases ?</p>Graph Theoryhttp://gateoverflow.in/130141/2-connected-graphFri, 19 May 2017 07:12:05 +0000Isomorphism and subgraph
http://gateoverflow.in/130078/isomorphism-and-subgraph
If there are two graphs G1 and G2 and both are Isomorphic to each other...Is G1 subset of G2?Graph Theoryhttp://gateoverflow.in/130078/isomorphism-and-subgraphThu, 18 May 2017 15:21:51 +0000Pigeonhole Counting
http://gateoverflow.in/130061/pigeonhole-counting
In a group of 10 people, where any two people are either friends or enemies, show that there are either 3 mutual friends or 4 mutual enemies and there are either 3 mutual enemies or 4 mutual friendsMathematical Logichttp://gateoverflow.in/130061/pigeonhole-countingThu, 18 May 2017 08:28:24 +0000Kenneth H.Rosen
http://gateoverflow.in/130039/kenneth-h-rosen
<p>For gate CSE/IT 2018 </p>
<table border="0" cellpadding="0" cellspacing="0">
<tbody>
<tr>
<th>Author Name</th>
<th>Edition</th>
<th> Relevant Chapters </th>
</tr>
</tbody>
</table>
<table border="0" cellpadding="0" cellspacing="0">
<tbody>
<tr>
<td>
<p> Rosen </p>
</td>
<td>
<p>7</p>
</td>
<td>
<p> 1,2,6-11</p>
</td>
</tr>
</tbody>
</table>
<p>is it covers all Engineering Mathematics topics or I need to read other books for remaining topics?</p>
<p>from chapters 1,2,6-11 (Discrete Maths, Probability, Graph Theory, Calculus, Linear Algebra) covers or not?</p>
<p>if not then please give me full detail as what read from where?from which book?full book or give chapter name. </p>
<p> </p>Mathematical Logichttp://gateoverflow.in/130039/kenneth-h-rosenThu, 18 May 2017 03:15:50 +0000Kenneth rosen chp 6 question 39 counting
http://gateoverflow.in/130005/kenneth-rosen-chp-6-question-39-counting
How many partial functions are there from a set with m elements to a set with n elements, where m and n are positive integers.<br />
<br />
Answer : (n+1)^m <br />
<br />
How . Can anyone please help?Combinatoryhttp://gateoverflow.in/130005/kenneth-rosen-chp-6-question-39-countingWed, 17 May 2017 14:54:04 +0000Kenneth rosen chapter 6 question 41 counting
http://gateoverflow.in/129991/kenneth-rosen-chapter-6-question-41-counting
A palindrome is a string whose reversal is identical to the string. how many bit strings of length n are palindromes ?Combinatoryhttp://gateoverflow.in/129991/kenneth-rosen-chapter-6-question-41-countingWed, 17 May 2017 13:00:29 +0000Kenneth rosen chapter 6 question 17 counting
http://gateoverflow.in/129976/kenneth-rosen-chapter-6-question-17-counting
How many strings of 5 ASCII characters contain the character @ atleast once ? [ NOTE : there are 128 ascii characters ] <br />
<br />
<br />
<br />
Answer is : 1,321,368,961<br />
<br />
Can anyone explain how ?Combinatoryhttp://gateoverflow.in/129976/kenneth-rosen-chapter-6-question-17-countingWed, 17 May 2017 11:15:26 +0000basic aptitude
http://gateoverflow.in/129883/basic-aptitude
<table>
<tbody>
<tr>
<td>
<p>12 chairs are arranged in a row and are numbered 1 to 12 4 men have to be seated in these chairs so that the chairs numbered 1 and 8 should be occupied and no two men occupy adjacent chairs.</p>
<p>Find the number of ways the task can be done.</p>
</td>
</tr>
</tbody>
</table>
<table>
<tbody>
<tr>
<td> </td>
<td><strong>A.</strong></td>
<td>
<p>360</p>
</td>
</tr>
<tr>
<td> </td>
<td><strong>B.</strong></td>
<td>
<p>384</p>
</td>
</tr>
<tr>
<td> </td>
<td><strong>C.</strong></td>
<td>
<p>432</p>
</td>
</tr>
<tr>
<td> </td>
<td><strong>D.</strong></td>
<td>
<p>470</p>
</td>
</tr>
</tbody>
</table>Combinatoryhttp://gateoverflow.in/129883/basic-aptitudeMon, 15 May 2017 14:03:54 +0000basic aptitude
http://gateoverflow.in/129878/basic-aptitude
<table>
<tbody>
<tr>
<td>
<p>The letter of the word LABOUR are permuted in all possible ways and the words thus formed are arranged as in a dictionary. What is the rank of the word LABOUR?</p>
</td>
</tr>
</tbody>
</table>
<table>
<tbody>
<tr>
<td> </td>
<td><strong>A.</strong></td>
<td>
<p>275</p>
</td>
</tr>
<tr>
<td> </td>
<td><strong>B.</strong></td>
<td>
<p>251</p>
</td>
</tr>
<tr>
<td> </td>
<td><strong>C.</strong></td>
<td>
<p>240</p>
</td>
</tr>
<tr>
<td> </td>
<td><strong>D.</strong></td>
<td>
<p>242</p>
</td>
</tr>
</tbody>
</table>
<p> can someone give me proper way to solve ?</p>Combinatoryhttp://gateoverflow.in/129878/basic-aptitudeMon, 15 May 2017 13:48:10 +0000permutation n combination
http://gateoverflow.in/129844/permutation-n-combination
There are 10 points in a plane ,no three of which are in the same straight line ,excepting 4 points ,which are collinear.<br />
<br />
find the 1)number of straight lines obtained from pairs of these points ;<br />
<br />
2)number of triangles that can be formed with the vertices as these pointsMathematical Logichttp://gateoverflow.in/129844/permutation-n-combinationMon, 15 May 2017 05:29:18 +0000Subsequence Theorem From Rosen.
http://gateoverflow.in/129834/subsequence-theorem-from-rosen
There is a theorem<br />
<br />
Every sequence of n^2 + 1 distinct real numbers contains a subsequence of length n + 1 that<br />
is either strictly increasing or strictly decreasing.<br />
<br />
Proof: Let a1, a2,...,an2+1 be a sequence of n^2 + 1 distinct real numbers.Associate an ordered<br />
pair with each term of the sequence, namely, associate (ik, dk) to the term ak, where ik is the<br />
length of the longest increasing subsequence starting at ak, and dk is the length of the longest<br />
decreasing subsequence starting at ak.<br />
Suppose that there are no increasing or decreasing subsequences of length n + 1. Then ik<br />
and dk are both positive integers less than or equal to n, for k = 1, 2,...,n^2 + 1. Hence, by the<br />
product rule there are n2 possible ordered pairs for (ik, dk). By the pigeonhole principle, two of<br />
these n^2 + 1 ordered pairs are equal. In other words, there exist terms as and at , with s<t<br />
such that is = it and ds = dt . We will show that this is impossible. Because the terms of the<br />
sequence are distinct, either as < at or as > at . If as < at , then, because is = it , an increasing<br />
subsequence of length it + 1 can be built starting at as, by taking as followed by an increasing<br />
subsequence of length it beginning at at . This is a contradiction. Similarly, if as > at , the same<br />
reasoning shows that ds must be greater than dt , which is a contradiction.<br />
<br />
<br />
<br />
<br />
<br />
My question is how n^2 ordered pair possible for (ik,dk) ??Combinatoryhttp://gateoverflow.in/129834/subsequence-theorem-from-rosenMon, 15 May 2017 03:12:13 +0000find complexity?
http://gateoverflow.in/129573/find-complexity
What is cyclomatic complexity of below program below:<br />
<br />
i=0; n=4;<br />
<br />
while(i<n-1)<br />
<br />
{j=i+1;<br />
<br />
while(j<n)<br />
<br />
{if(A[i]< A[j]) swap (A[i],A[j]);}<br />
<br />
i=i+1;<br />
<br />
}<br />
<br />
A)3 B)4 C)5 D)6Graph Theoryhttp://gateoverflow.in/129573/find-complexitySun, 14 May 2017 04:03:04 +0000GATE Graph Theory
http://gateoverflow.in/129447/gate-graph-theory
Let G = (V, E) be a directed graph where V is the set of vertices and E the set of edges. Then which one of the following graphs has the same strongly connected components as G?<br />
<br />
( A ) G1 = (V, E1) where E1 = {(u, v) | (u, v) ∉ E}<br />
( B ) G2 = (V, E2) where E2 = {(u, v) | (v, u) ∉ E}<br />
( C ) G3 = (V, E3) where E3 = {(u, v) | there ish a path of length ≤ 2 from u to v in E}<br />
( D ) G4 = (V4, E) where V4 is the set of vertices in G which are not isolated<br />
<br />
Can anyone give a detailed answer to this question, please? :)Graph Theoryhttp://gateoverflow.in/129447/gate-graph-theoryFri, 12 May 2017 19:24:26 +0000Divisibility Test of 11
http://gateoverflow.in/129406/divisibility-test-of-11
<p>This is the statement for Divisibility test of 11.</p>
<blockquote>
<p>Add and subtract digits in an alternating pattern (add digit, subtract next digit, add next digit, etc). Then check if that answer is divisible by 11.</p>
</blockquote>
<p>This is the proof that I found :</p>
<p> If x is divisible by 11, then x ≡ 0 (mod 11). Thus $x_{n} + 10x_{n−1} + 100x_{n−2} + . . . + 10^{n-1}x_{1} ≡ 0 (mod 11)$.</p>
<p>But $x_{n} + 10x_{n−1} + 100x_{n−2} +. . .+ 10^{n−1}x_{1} ≡ x_{n} −x_{n−1} +x_{n−2} −. . .+ (−1)^{n−1}x_{1} ≡ 0 (mod 11)$. Which means that the alternating 2 sum of the digits of the number x,$x_{n} − x_{n−1} + x_{n−2}$ − . . ., is divisible by 11. The argument can be easily reversed.</p>
<p>-----------------------------------------------------</p>
<p>Now, I didn't understand the proof starting from <em>But</em>.</p>Mathematical Logichttp://gateoverflow.in/129406/divisibility-test-of-11Fri, 12 May 2017 13:27:50 +0000maths
http://gateoverflow.in/129390/maths
A is a set containing n elements .A subset P of A is chosen at random .Th set A i reconstructed by replacing the elements of P.A subset Q is again chosen at random .Find the probability that<br />
<br />
1.Pand Q are disjoint sets<br />
<br />
2.P=Q<br />
<br />
3.P U Q=A<br />
<br />
4.P intersection Q contains just one elementMathematical Logichttp://gateoverflow.in/129390/mathsFri, 12 May 2017 11:26:32 +0000maths
http://gateoverflow.in/129382/maths
Each coefficient in the equation ax^2+bx+c=0 is determined by throwing an ordinary six faced die.Find the probability that the equation will hav real rootsMathematical Logichttp://gateoverflow.in/129382/mathsFri, 12 May 2017 11:08:10 +0000maths
http://gateoverflow.in/129379/maths
In how many ways three girls and nine boys can be seated int two vans each having numbered seats ,3 in the front and and 4 at the back ?<br />
<br />
How many arrangements are possible if 3 girls sit together in back row on adjacent seats?Combinatoryhttp://gateoverflow.in/129379/mathsFri, 12 May 2017 10:58:33 +0000matrices
http://gateoverflow.in/129372/matrices
<p>Let A be a real $2 \times 2$ matrix.If $5 + 3\iota$ is an eigen value of A, then det(A)</p>
<p>(A)equals 4</p>
<p>(B)equals 8</p>
<p>(C)equals 16</p>
<p><img alt="" height="166" src="http://gateoverflow.in/?qa=blob&qa_blobid=3112571894370956011" width="1228"></p>
<p> </p>Mathematical Logichttp://gateoverflow.in/129372/matricesFri, 12 May 2017 10:28:24 +0000Rosen Doubt
http://gateoverflow.in/129359/rosen-doubt
<p>Express the specification “<strong>The automated reply cannot be sent when the file system is full”</strong></p>
<p>using logical connectives.</p>
<p> </p>Mathematical Logichttp://gateoverflow.in/129359/rosen-doubtFri, 12 May 2017 08:20:38 +0000Graph Theory
http://gateoverflow.in/129355/graph-theory
algorithm to find more than one path between any two vertices of a graph G=(V,E) , with a complexity of O(VE) ?Graph Theoryhttp://gateoverflow.in/129355/graph-theoryFri, 12 May 2017 08:04:59 +0000The gatebook
http://gateoverflow.in/129333/the-gatebook
Total order relation is Lattice or not please explain?Set Theory & Algebrahttp://gateoverflow.in/129333/the-gatebookFri, 12 May 2017 02:50:58 +0000keneth r rosen discrete mathematics
http://gateoverflow.in/129180/keneth-r-rosen-discrete-mathematics
the relation R is partial order on the set Z where, R is defined as, a R b iff a=2b.<br />
<br />
how to prove it.Set Theory & Algebrahttp://gateoverflow.in/129180/keneth-r-rosen-discrete-mathematicsWed, 10 May 2017 13:49:11 +0000keneth r rosen discrete mathematics
http://gateoverflow.in/129179/keneth-r-rosen-discrete-mathematics
<p>IF H be a subgroup of a group G then how to prove that the relation</p>
<p>R= {(x,y): x,y belong to G, x<sup>-1</sup>ybelongs to H} is an equivalence relation.</p>
<p>Please help as soon as possible.</p>Mathematical Logichttp://gateoverflow.in/129179/keneth-r-rosen-discrete-mathematicsWed, 10 May 2017 13:47:09 +0000keneth r rosen discrete mathematics
http://gateoverflow.in/129178/keneth-r-rosen-discrete-mathematics
<p>In a group G, how to prove that (a.b)<sup>-1 </sup>= b<sup>-1</sup>. a<sup>-1 </sup> for all a,b belongs to G.</p>
<p> </p>
<p> </p>Mathematical Logichttp://gateoverflow.in/129178/keneth-r-rosen-discrete-mathematicsWed, 10 May 2017 13:39:36 +0000keneth r rosen discrete mathematics
http://gateoverflow.in/129177/keneth-r-rosen-discrete-mathematics
how to prove lagrange's theorem in groups?Mathematical Logichttp://gateoverflow.in/129177/keneth-r-rosen-discrete-mathematicsWed, 10 May 2017 13:35:34 +0000basic aptitude
http://gateoverflow.in/129131/basic-aptitude
<table>
<tbody>
<tr>
<td>
<p>Ten different letters of alphabet are given, words with 5 letters are formed from these given letters. Then, the number of words which have at least one letter repeated is:</p>
</td>
</tr>
</tbody>
</table>
<table>
<tbody>
<tr>
<td> </td>
<td><strong>A.</strong></td>
<td>
<p>69760</p>
</td>
</tr>
<tr>
<td> </td>
<td><strong>B.</strong></td>
<td>
<p>30240</p>
</td>
</tr>
<tr>
<td> </td>
<td><strong>C.</strong></td>
<td>
<p>99748</p>
</td>
</tr>
<tr>
<td> </td>
<td><strong>D.</strong></td>
<td>
<p>42386</p>
</td>
</tr>
</tbody>
</table>
<p> </p>
<p>i got ans from the method totol words - no word repeated , but if i want to do with general method means 10*10*9*8*7 *5!/2! + 10*10*10*9*8*5!/3! + 10*10*10*10*9*5!/4! + 10*10*10*10*!0 from this getting different ans where is going wrong ? someone verify pls </p>Combinatoryhttp://gateoverflow.in/129131/basic-aptitudeWed, 10 May 2017 06:22:38 +0000Graph theory
http://gateoverflow.in/129113/graph-theory
Which is the best book for studying GATE CS Graph theory?Graph Theoryhttp://gateoverflow.in/129113/graph-theoryWed, 10 May 2017 04:00:03 +0000Graph theory and Applications Bondy and Murty Exercise Qn 1.9
http://gateoverflow.in/129036/graph-theory-and-applications-bondy-and-murty-exercise-qn-1
<p>A k partite graph is one where vertex set can be partitioned into k subsets so that no edge has both end in any one subset.</p>
<p>A complete k partite graph is one that is simple and in which each vertex is joined to every other vertex that is not in the same subset. The complete m-partite graph on n vertices in which each part has either floor(n/m) or ceil(n/m) vertices is denoted by T<sub>m,n</sub> . Show that</p>
<p>a) | E(T<sub>m,n</sub>) | = $\binom{n-k}{2} + (m-1)\binom{k+1}{2} , k = \left \lfloor n/m \right \rfloor$</p>
<p>b) If G is a complete m-partite graph on n vertices then | E(G) | <= | E(T<sub>m,n</sub>)|, with equality only if G isomorphic to T<sub>m,n</sub></p>Graph Theoryhttp://gateoverflow.in/129036/graph-theory-and-applications-bondy-and-murty-exercise-qn-1Tue, 09 May 2017 16:09:49 +0000Thesis papers exclusively!!
http://gateoverflow.in/129035/thesis-papers-exclusively
When you find difficulty with writing a thesis paper, get custom written thesis from thesis writing service online. Writing services accessible online have a professional team of academic writers and they assign your order to the most suitable writer in order to make your paper custom written. Most of the best academic writing service promise thesis papers exclusively written for you and never resell the paper written for you. So, seek out writing help from the professionals in the field.Mathematical Logichttp://gateoverflow.in/129035/thesis-papers-exclusivelyTue, 09 May 2017 15:59:49 +0000best advantages of seeking thesis writing help from online service
http://gateoverflow.in/129034/best-advantages-seeking-thesis-writing-help-online-service
<p>Since thesis writing is a challenging task, nearly all the students will look for someone to help them expertly. At present, the learners can find a plenty of academic writing services online and observably, writing services can lend a hand to you to complete your thesis in an effective manner. One of the best advantages of seeking thesis writing help from <a rel="nofollow" href="https://www.bestessaywritingservice.co/">best essay writing service</a> is that all custom papers and essays are written by experienced writers in proportion to your orders and requirements. As a result, you can obtain unique thesis paper and exclude any chance of plagiarism.</p>Mathematical Logichttp://gateoverflow.in/129034/best-advantages-seeking-thesis-writing-help-online-serviceTue, 09 May 2017 15:54:49 +0000ISRO2017-22
http://gateoverflow.in/128691/isro2017-22
<p>Which one of the following Boolean expressions is NOT a tautology?</p>
<ol style="list-style-type:upper-alpha">
<li>$((a \rightarrow b) \wedge (b \rightarrow c)) \rightarrow (a \rightarrow c)$</li>
<li>$(a \leftrightarrow c) \rightarrow (\sim b\rightarrow (a\wedge c))$</li>
<li>$(a\wedge b \wedge c)\rightarrow (c \vee a)$</li>
<li>$a\rightarrow (b\rightarrow a)$</li>
</ol>Mathematical Logichttp://gateoverflow.in/128691/isro2017-22Sun, 07 May 2017 20:44:11 +0000#rosen , #counting , #5.1 , 41(a)
http://gateoverflow.in/128608/%23rosen-%23counting-%235-1-41-a
in how many ways can a photographer at a wedding arrange 6 people in a row from a group of 10 people, where the bride and the groom are among these 10 people , if<br />
<br />
a) the bride must next to the groom<br />
<br />
my solution is since given that bride and groom must be next to each other then now we have to select 4 person from 8 that is 8c4 now we have to arrange these people since bride and groom next to each other then take BG as one block and rest four __ , __ , __ , __ ,<br />
<br />
now arranging BG , __ , __ ,__, __ will take 5! , and arranging BG mutually is 2! ,<br />
<br />
so total ways is 8c4*5!*2!<br />
<br />
but answer is given 240 (rosen )Combinatoryhttp://gateoverflow.in/128608/%23rosen-%23counting-%235-1-41-aSun, 07 May 2017 17:51:30 +0000ISRO2017-9
http://gateoverflow.in/128555/isro2017-9
<p>The symmetric difference of sets $A=\{1,2, 3,4, 5, 6, 7, 8\}$ and $B= \{1, 3, 5, 6, 7,8,9\}$ is:</p>
<ol style="list-style-type: upper-alpha;">
<li>$\{1, 3, 5, 6, 7,8\}$</li>
<li>$\{2, 4, 9\}$</li>
<li>$\{2, 4\}$</li>
<li>$\{1, 2, 3, 4, 5, 6, 7, 8, 9\}$</li>
</ol>Set Theory & Algebrahttp://gateoverflow.in/128555/isro2017-9Sun, 07 May 2017 16:50:47 +0000keneth r rosen
http://gateoverflow.in/128476/keneth-r-rosen
<p>HOW TO SOLVE THIS USING BOOLEAN ALGEBRA; <img alt="" height="71" src="http://gateoverflow.in/?qa=blob&qa_blobid=986322319398299267" width="199"></p>Mathematical Logichttp://gateoverflow.in/128476/keneth-r-rosenSun, 07 May 2017 13:40:59 +0000keneth r rosen
http://gateoverflow.in/128475/keneth-r-rosen
<p>WHAT IS DNF <a rel="nofollow" href="https://en.wikipedia.org/wiki/Disjunctive_normal_form" target="_blank">Disjunctive normal form IN BOOLEAN ALGEBRA?</a></p>Mathematical Logichttp://gateoverflow.in/128475/keneth-r-rosenSun, 07 May 2017 13:39:09 +0000keneth r rosen
http://gateoverflow.in/128474/keneth-r-rosen
<p>how to find / what will be the DNF(<a rel="nofollow" href="https://en.wikipedia.org/wiki/Disjunctive_normal_form" target="_blank">Disjunctive normal form</a>) of :<img alt="" height="79" src="http://gateoverflow.in/?qa=blob&qa_blobid=977276020805951016" width="381"></p>Mathematical Logichttp://gateoverflow.in/128474/keneth-r-rosenSun, 07 May 2017 13:37:53 +0000keneth r rosen
http://gateoverflow.in/128473/keneth-r-rosen
<p>how to solve this using rules of boolean algebra: </p>
<p><img alt="" height="104" src="http://gateoverflow.in/?qa=blob&qa_blobid=2295465886290990612" width="337"></p>Mathematical Logichttp://gateoverflow.in/128473/keneth-r-rosenSun, 07 May 2017 13:34:25 +0000keneth r rosen
http://gateoverflow.in/128471/keneth-r-rosen
how to prove that sum of all the vertices in a graph G is equal to twice the number of edges in G.<br />
<br />
please explain step by step .Graph Theoryhttp://gateoverflow.in/128471/keneth-r-rosenSun, 07 May 2017 13:28:40 +0000keneth r rosen
http://gateoverflow.in/128470/keneth-r-rosen
<p>how to prove that graph G with<strong> </strong>e= v - 1 that has no circuit is a tree.</p>Graph Theoryhttp://gateoverflow.in/128470/keneth-r-rosenSun, 07 May 2017 13:26:36 +0000keneth r rosen
http://gateoverflow.in/128469/keneth-r-rosen
If a,b be elements of a Boolean algebra then how to show that (a∨b)' = a' ∧ b'.<br />
<br />
please explain step by step in easiest way possibleMathematical Logichttp://gateoverflow.in/128469/keneth-r-rosenSun, 07 May 2017 13:23:32 +0000