GATE Overflow - Recent questions in Mathematical Logic
http://gateoverflow.in/questions/mathematics/discrete-mathematics/mathematical-logic
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 +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 +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 +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 +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 +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 +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 +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/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 +0000how to remove ambiguity that whether should take lower or upper shield in counting problem
http://gateoverflow.in/128445/remove-ambiguity-whether-should-lower-shield-counting-problem
how many positive integer between 50 and 100 ,<br />
<br />
(a) divisible by 7<br />
(b) divisible by 11<br />
(c) divisible by 7 and 11 ?<br />
<br />
people generally answer this question as<br />
<br />
(a) lowershield [((100-50)-1 )/7] = 7 , yess its true the no is 56 , 63 , 70, 84, 91 , 98 <br />
(b) lowershield [((100-50)-1 )/11] = 4 , oops its not true the no is 55,66,77,88,99<br />
<br />
(c) lowershield [((100-50)-1 )/lcm(7,11)] = 0 , oops its not true the no is 77<br />
<br />
if u will say to take uppershield then lets come<br />
<br />
(a) uppershield[((100-50)-1)/7]=7 , yess its true<br />
<br />
(b) uppershield[((100-50)-1)/11]=5 , yess its true<br />
<br />
(c) uppershield[((100-50)-1)/lcm(7,11)]=1 , yess its true<br />
<br />
now come to another question<br />
<br />
how many no is divisible between 5 to 31 is divisible by 4 ?<br />
<br />
case1 : loweshield [((31-5)-1)/4]=6 , yess its true 8,12,16,20,24,28<br />
<br />
case 2 : uppershierld [((31-5)-1/4)]=7 , oops its wrong<br />
<br />
how can we remove this ambiguity ?<br />
<br />
if u will argue that check the no ? but we have to check for large no like 50 to 300000 then how can u count ?<br />
<br />
my doubt is , is any way to remove this ambiguity ?Mathematical Logichttp://gateoverflow.in/128445/remove-ambiguity-whether-should-lower-shield-counting-problemSun, 07 May 2017 09:54:44 +0000Kenneth Rosen Ch 6 Counting
http://gateoverflow.in/128256/kenneth-rosen-ch-6-counting
#discrete<br />
<br />
6 runners are in a 100 yard dash. Find the ways possible for 3 medals to be awarded if ties are possible.Mathematical Logichttp://gateoverflow.in/128256/kenneth-rosen-ch-6-countingFri, 05 May 2017 17:44:44 +0000Rosen Mathematical Logic Example Simple question with "Only if"
http://gateoverflow.in/127998/rosen-mathematical-logic-example-simple-question-with-only
<p>You can access the internet <strong>only if</strong> you are a computer science major or you are not a freshman.
<br>
<br>
You can access the internet (p)
<br>
you are a computer science major (q)
<br>
you are a freshman (r)
<br>
<br>
Why the ans is <strong>p-> (q v r ) </strong>?
<br>
Why not <strong>(q v r ) -> p </strong> ?</p>Mathematical Logichttp://gateoverflow.in/127998/rosen-mathematical-logic-example-simple-question-with-onlyWed, 03 May 2017 20:34:16 +0000thegatebook
http://gateoverflow.in/127975/thegatebook
22) S1: A formula is valid iff its complement is not satisfiable<br />
<br />
S2: A formula is satisfiable iff its complement is not valid.<br />
<br />
Which statement is/are true?<br />
<br />
<br />
<br />
a) Only S1 b) Only S2 c) both S1 and S2 d) noneMathematical Logichttp://gateoverflow.in/127975/thegatebookWed, 03 May 2017 19:07:16 +0000Discrete Mathematics Thegatebook
http://gateoverflow.in/127913/discrete-mathematics-thegatebook
Which of the following propositional logic formulae is TRUE when exactly two of p,q and r are TRUE?<br />
<br />
(A) ((p↔q)∧r)∨(p∧q∧¬r))<br />
<br />
B (¬(p↔q)∧r)∨(p∧q∧¬r))<br />
<br />
C ((p↔q)∧r)∨(p∧q∧¬r))<br />
<br />
D (¬(p↔q)∧r)∧(p∧q∧¬r))Mathematical Logichttp://gateoverflow.in/127913/discrete-mathematics-thegatebookWed, 03 May 2017 11:50:17 +0000Discrete Mathematics
http://gateoverflow.in/127712/discrete-mathematics
21) S1: If P, Q, R are three compound propositions and If P does not logically equivalent to Q and Q does not logically equivalent to R then P does not logically equivalent to R<br />
S2: If P, Q, R are three compound propositions and P ⇔ Q and Q ⇔ R then<br />
P ⇔R<br />
a) Only S1 b) Only S2 c) both S1 and S2 d) neither S1 nor S2Mathematical Logichttp://gateoverflow.in/127712/discrete-mathematicsMon, 01 May 2017 20:24:08 +0000Discrete Mathematics Thegatebook
http://gateoverflow.in/127711/discrete-mathematics-thegatebook
Q1.How to write in Predicate Logic<br />
<br />
"Everyone is Liked by Someone"Mathematical Logichttp://gateoverflow.in/127711/discrete-mathematics-thegatebookMon, 01 May 2017 20:22:04 +0000Discrete Mathematics Thegatebook
http://gateoverflow.in/127670/discrete-mathematics-thegatebook
22)Which one is the correct<br />
<br />
S1: A formula is valid iff its complement is not satisfiable<br />
S2: A formula is satisfiable iff its complement is not valid.<br />
a) Only S1 b) Only S2 c) both S1 and S2 d) noneMathematical Logichttp://gateoverflow.in/127670/discrete-mathematics-thegatebookMon, 01 May 2017 17:31:29 +0000Discrete Mathematics Thegatebook
http://gateoverflow.in/127669/discrete-mathematics-thegatebook
20) If S d is a dual of S then (S d )d ⇔<br />
a) ~S b) S c) T d) FMathematical Logichttp://gateoverflow.in/127669/discrete-mathematics-thegatebookMon, 01 May 2017 17:28:23 +0000Discrete Mathematics Thegatebook
http://gateoverflow.in/127668/discrete-mathematics-thegatebook
10) Which of the following inference system is invalid?<br />
a) R---> S, ~S |- ~R<br />
b) ~R, P----> Q, Q -----> R |- ~P<br />
c) ~R (S --------> ~T), ~R ∨ W, ~P --------> S, ~W |- T ------> P<br />
d) P ∧ Q -----> ~T, W ∨ R, W -----> P, R -----> Q |- (W ∨ R) --------> ~TMathematical Logichttp://gateoverflow.in/127668/discrete-mathematics-thegatebookMon, 01 May 2017 17:26:19 +0000Discrete Mathematics Thegatebook
http://gateoverflow.in/127664/discrete-mathematics-thegatebook
Q1. Which of the following arguments are invalid?<br />
S1: If it rains Erick will be sick<br />
It did not rain<br />
Erick was not sick<br />
S2: If I study then I will not fail mathematics<br />
If I do not play basketball, then I will study<br />
But I failed mathematics<br />
Therefore I must have played basketball<br />
a) Only S1 b) Only S2 c) both S1 and S2 d) neither S1 nor S2Mathematical Logichttp://gateoverflow.in/127664/discrete-mathematics-thegatebookMon, 01 May 2017 17:20:51 +0000Liar paradox
http://gateoverflow.in/127517/liar-paradox
<p>Which of the following statements is true?</p>
<ol>
<li>There are no true statements.</li>
<li>There is only 1 false statement.</li>
<li>There are only 2 false statements . </li>
<li>There are only 3 false statements . </li>
<li>There are only 4 false statements.</li>
</ol>
<p>The question seems complete as it is an example of the liar paradox, but looking up into the problem I'm finding no solution to it. Since it was asked in exam I expect some option to be correct or else how are they gonna grade the people attempting it? Any explainations would be welcome.</p>Mathematical Logichttp://gateoverflow.in/127517/liar-paradoxSun, 30 Apr 2017 17:36:11 +0000Pgee 2017
http://gateoverflow.in/127515/pgee-2017
<p>What is the equivalent de morgan's representation of the logic statement (c!=n && q <=5) ?</p>
<ol>
<li>! ( c!=n || q>=5)</li>
<li>! ( c==n || q>=5)</li>
<li>! ( c!=n || q>5)</li>
<li>! ( c==n || q>5)</li>
</ol>Mathematical Logichttp://gateoverflow.in/127515/pgee-2017Sun, 30 Apr 2017 17:23:07 +0000Gate 2010,,Quetion number 26,,
http://gateoverflow.in/126895/gate-2010-quetion-number-26
Torque exerted on a flywheel over a cycle is listed in the table .flywheel energy (in j per unit cycle) using simpson's rule isMathematical Logichttp://gateoverflow.in/126895/gate-2010-quetion-number-26Tue, 25 Apr 2017 10:36:15 +0000what will be fuzzy set ?
http://gateoverflow.in/126412/what-will-be-fuzzy-set
<p><img alt="" src="http://gateoverflow.in/?qa=blob&qa_blobid=12093664083042897413"></p>Mathematical Logichttp://gateoverflow.in/126412/what-will-be-fuzzy-setFri, 21 Apr 2017 13:21:19 +0000what will be closed interval fuzzy alpha cut
http://gateoverflow.in/126411/what-will-be-closed-interval-fuzzy-alpha-cut
<p><img alt="" src="http://gateoverflow.in/?qa=blob&qa_blobid=13058502573838744628"></p>Mathematical Logichttp://gateoverflow.in/126411/what-will-be-closed-interval-fuzzy-alpha-cutFri, 21 Apr 2017 13:17:33 +0000Fuzzy doubt
http://gateoverflow.in/126410/fuzzy-doubt
<p><img alt="" src="http://gateoverflow.in/?qa=blob&qa_blobid=5037012022155623760"></p>Mathematical Logichttp://gateoverflow.in/126410/fuzzy-doubtFri, 21 Apr 2017 13:14:55 +0000Which fuzzy set is fuzzy number ?
http://gateoverflow.in/126407/which-fuzzy-set-is-fuzzy-number
<p><img alt="" src="http://gateoverflow.in/?qa=blob&qa_blobid=7520577286953440950"></p>Mathematical Logichttp://gateoverflow.in/126407/which-fuzzy-set-is-fuzzy-numberFri, 21 Apr 2017 13:11:01 +0000DMS - Kenneth Rosen Ex. 1.4 10
http://gateoverflow.in/126282/dms-kenneth-rosen-ex-1-4-10
<p>Let F (x,y) be the statement such as x can fool y .where the domain consists of all people in world .
<br>
<br>
Express following statement using quantifiers
<br>
<br>
<br>
<span class="marker"><strong>There is exactly one person whom everybody can fool </strong></span>
<br>
<br>
</p>Mathematical Logichttp://gateoverflow.in/126282/dms-kenneth-rosen-ex-1-4-10Thu, 20 Apr 2017 11:25:07 +0000DMS - Rosen Exercise 1.4 - 8
http://gateoverflow.in/126182/dms-rosen-exercise-1-4-8
<p>Let Q(x, y) be the statement “student x has been a contestant
<br>
on quiz show y.” Express 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.
<br>
<br>
* <span class="marker"><strong>At least two students from your school have been contestants
<br>
on Jeopardy.</strong></span></p>Mathematical Logichttp://gateoverflow.in/126182/dms-rosen-exercise-1-4-8Wed, 19 Apr 2017 11:52:10 +0000Kenneth Rosen- Mathematical logic
http://gateoverflow.in/126106/kenneth-rosen-mathematical-logic
Express below using quantifiers :<br />
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"At least one mail message among the non-empty set of messages, can be saved if there is a disk with more than 10 kilobytes of free space"<br />
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Answer was given as :<br />
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(∃x F(x,10))→∃x S(x)<br />
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Where F(x,y) Disk x has more than y kilobytes of free space<br />
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S(x) Mail message x can be saved.<br />
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Can somebody explain me the solution?Mathematical Logichttp://gateoverflow.in/126106/kenneth-rosen-mathematical-logicTue, 18 Apr 2017 18:32:43 +0000Kenneth Rosen - Mathematical logic
http://gateoverflow.in/126105/kenneth-rosen-mathematical-logic
Let T(x,y) mean that student x likes cuisine y, where the domain for x consists of all students at your school and the domain y consists of all cuisines.<br />
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What is meant by the below expression?<br />
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∀x∀z∃y ((x≠z)→ ∼(T(x,y) ^ T(z,y)))Mathematical Logichttp://gateoverflow.in/126105/kenneth-rosen-mathematical-logicTue, 18 Apr 2017 18:27:22 +0000First Order Validities
http://gateoverflow.in/126012/first-order-validities
I'm having a hard time solving first order formulae for checking validities. Every question I see here is either assuming some statements or writing generic statements like: for all x, if p holds then q holds etc...<br />
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Can anyone tell me another methods (may be using quantifier inferences or any other method) or suggest some readings on this topic.<br />
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Thanks Guys...Mathematical Logichttp://gateoverflow.in/126012/first-order-validitiesMon, 17 Apr 2017 23:10:13 +0000Chapter 1: Kenneth Rosen , page: 17;eg:2
http://gateoverflow.in/126009/chapter-1-kenneth-rosen-page-17-eg-2
In Rosen, page:17,example:2, <br />
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q:"you can ride roller coaster"<br />
r:"you are under 4 feet tall"<br />
s:"you are older than 16"<br />
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For representing" you cannot ride the roller coaster if you are under 4 feet tall unless you are older than 16 years old"<br />
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(-q) if (r unless s)<br />
(-q) if (-s --> r)<br />
( -s --> r ) --> (-q) is the answer I"m getting, however, in the example he replaced unless with and not and gave answer (r ^ -s ) --> -q;<br />
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Now, which is correct?Mathematical Logichttp://gateoverflow.in/126009/chapter-1-kenneth-rosen-page-17-eg-2Mon, 17 Apr 2017 22:59:35 +0000