GATE Overflow for GATE CSE - Recent questions tagged discrete-mathematics
https://gateoverflow.in/tag/discrete-mathematics
Powered by Question2AnswerDiscrete mathematics kenneth rosen
https://gateoverflow.in/389807/discrete-mathematics-kenneth-rosen
Determine whether the premises “If I do not leave my home early or get stuck in a traffic jam, I will be late to my class and get scolded by my teacher”, “If I am late to my class, I will miss the attendance for the day”, and “I have gotten my attendance today” lead to the conclusion “Therefore, I have left my home early today”. Explain which rules of inference are used for each step.Mathematical Logichttps://gateoverflow.in/389807/discrete-mathematics-kenneth-rosenTue, 29 Nov 2022 19:17:07 +0000problem from Kenneth Rosen's Discrete Mathematics and its Applications, Section 1.5 - 1.7
https://gateoverflow.in/389521/problem-kenneth-discrete-mathematics-applications-section
<p>Please solve the question. </p>
<p><strong>Question: Express each of these system specifications using predicates, quantifiers, and logical<br>
connectives.</strong></p>
<p>a. Any user with a Gmail account can access services from any Google products.</p>
<p>b. There is a database which contains the records of all the students in this university.</p>
<p>c. No servers can be down simultaneously during a power failure.</p>
<p>d. There is a node whose adjacent nodes are not connected to each other.<br>
</p>Unknown Categoryhttps://gateoverflow.in/389521/problem-kenneth-discrete-mathematics-applications-sectionSun, 27 Nov 2022 16:53:57 +0000Solve the simultaneous recurrence relations
https://gateoverflow.in/389383/solve-the-simultaneous-recurrence-relations
an = an−1 + bn−1<br />
bn = an−1 − bn−1<br />
with a0 = 1 and b0 = 2.Combinatoryhttps://gateoverflow.in/389383/solve-the-simultaneous-recurrence-relationsFri, 25 Nov 2022 17:44:20 +0000gateforum
https://gateoverflow.in/388918/gateforum
<p><img alt="" src="https://gateoverflow.in/?qa=blob&qa_blobid=3503592563800676053"></p>Mathematical Logichttps://gateoverflow.in/388918/gateforumSat, 19 Nov 2022 12:42:34 +0000gateforum
https://gateoverflow.in/388917/gateforum
<p><img alt="" src="https://gateoverflow.in/?qa=blob&qa_blobid=3503592563800676053"></p>Mathematical Logichttps://gateoverflow.in/388917/gateforumSat, 19 Nov 2022 12:41:48 +0000graph theory ,discrete math
https://gateoverflow.in/388839/graph-theory-discrete-math
how many subgraph with atleast 1 vertex does k2 have? (graph theory question)Mathematical Logichttps://gateoverflow.in/388839/graph-theory-discrete-mathFri, 18 Nov 2022 05:49:47 +0000Madeasy Test series 2023 Discrete Maths
https://gateoverflow.in/387285/madeasy-test-series-2023-discrete-maths
<p><img alt="" src="https://gateoverflow.in/?qa=blob&qa_blobid=14494547340703992786"></p>Mathematical Logichttps://gateoverflow.in/387285/madeasy-test-series-2023-discrete-mathsWed, 02 Nov 2022 18:27:35 +0000Ace Academy Test Series Qn#7
https://gateoverflow.in/387055/ace-academy-test-series-qn%237
<p>A hash function h maps 16-bit inputs to 8 bit hash values. What is the largest k such that in any set of 1000 inputs, there are atleast k inputs that h maps to the same hash value?</p>
<ol style="list-style-type:lower-alpha" type="a">
<li>3</li>
<li>4</li>
<li>10</li>
<li>64</li>
</ol>DShttps://gateoverflow.in/387055/ace-academy-test-series-qn%237Sun, 30 Oct 2022 09:54:15 +0000Ace Academy Test Series
https://gateoverflow.in/387054/ace-academy-test-series
<p>A hash function h maps 16-bit inputs to 8 bit hash values. What is the largest k such that in any set of 1000 inputs, there are atleast k inputs that h maps to the same hash value?</p>
<ol style="list-style-type:lower-alpha" type="a">
<li>3</li>
<li>4</li>
<li>10</li>
<li>64</li>
</ol>DShttps://gateoverflow.in/387054/ace-academy-test-seriesSun, 30 Oct 2022 09:53:45 +0000Let 𝐼(𝑥)be the statement “𝑥has an Internet connection” and 𝐶(𝑥,𝑦)be the statement “𝑥and𝑦have chatted over the Internet,” where the domain for the variables 𝑥and 𝑦consists of all students in your class. Use quantifiers to express the followingstatement:“Everyone in your class with an Internet connection has chatted over the Internet with at least one other student in your class.
https://gateoverflow.in/386896/connection-variables-quantifiers-followingstatement-connection
Mathematical Logichttps://gateoverflow.in/386896/connection-variables-quantifiers-followingstatement-connectionSat, 29 Oct 2022 10:02:58 +0000Translate the given statement into propositional logicexpressions:“A man qualifies for the marathon if his best previous time is less than 3 hours and a woman qualifies for the marathon if her best previous time is less than 3.5 hours.
https://gateoverflow.in/386894/translate-statement-propositional-logicexpressions-qualifies
Mathematical Logichttps://gateoverflow.in/386894/translate-statement-propositional-logicexpressions-qualifiesSat, 29 Oct 2022 10:02:08 +0000KENNITH ROSEN LATTICE
https://gateoverflow.in/383808/kennith-rosen-lattice
Find a compatible total order for the divisibility relation<br />
on the set {1, 2, 3, 6, 8, 12, 24, 36}.Set Theory & Algebrahttps://gateoverflow.in/383808/kennith-rosen-latticeMon, 26 Sep 2022 06:45:33 +0000Gate At Zeal
https://gateoverflow.in/383087/gate-at-zeal
Question → If (G,*) is a group of order 960 and there exist a in G such that a^m=e for some integer m<=960 where e is identity element of G then total number of possible value of m is___________<br />
<br />
<br />
<br />
Answer==28Set Theory & Algebrahttps://gateoverflow.in/383087/gate-at-zealSat, 17 Sep 2022 10:58:31 +0000PhD Admissions Written Test (Basic)
https://gateoverflow.in/382697/phd-admissions-written-test-basic
Let x1, x2, ...x8 be 8 propositional variables. Let · represent AND connective ⊕ represent the Exclusive-or connective.<br />
<br />
The number of satisfying assignments of the formula x1 ⊕ x2 ⊕ ...x8 is _________________<br />
<br />
The number of satisfying assignments of the formula (x1·x2) ⊕ (x3·x4)... ⊕ (x7·x8) is __________________Mathematical Logichttps://gateoverflow.in/382697/phd-admissions-written-test-basicSun, 11 Sep 2022 05:17:18 +0000igate test series
https://gateoverflow.in/382385/igate-test-series
Selection of how many integers from the first ten positive integers (1, 2, ...) guarantees that there must be a pair of these integers with a sum equal to 11 ?Combinatoryhttps://gateoverflow.in/382385/igate-test-seriesTue, 06 Sep 2022 19:15:35 +0000Predicate Translation
https://gateoverflow.in/382336/predicate-translation
<p><em><strong>S(x):</strong></em> <strong>x is a Student</strong><br>
<strong><em>P(x):</em></strong> <strong>x is a Professor</strong><br>
<em><strong>A(x, y):</strong></em> <strong>x has asked a question to y<br>
Domain not given, so we have to think about default domain</strong><br>
<strong>Q1)</strong> Translate <strong>“There is a student who has asked every professor a question”</strong><br>
<strong>Q2)</strong> Translate <strong>“There is a professor who has asked every student a question”</strong><br>
<strong>Q3)</strong> Translate <strong>“There is a professor who has been asked a question by every student”</strong><br>
<strong>Q4)</strong> Translate <strong>“There is a student who has been asked a question by every professor”</strong></p>Mathematical Logichttps://gateoverflow.in/382336/predicate-translationTue, 06 Sep 2022 06:03:30 +0000Mathematics for Natural Science
https://gateoverflow.in/379383/mathematics-for-natural-science
Let y in the form of $a + bi$, where $a$ and $b$ are real numbers, be the cubic roots of complex number $z^{20},$ where $z=\frac{2}{4 + 3i}.$ Find $a + b.$Combinatoryhttps://gateoverflow.in/379383/mathematics-for-natural-scienceFri, 29 Jul 2022 05:28:30 +0000Mathematics for Natural Science
https://gateoverflow.in/379382/mathematics-for-natural-science
Prove that $2n < (n + 1)!, $ for all $ n \geq 3.$Combinatoryhttps://gateoverflow.in/379382/mathematics-for-natural-scienceFri, 29 Jul 2022 05:24:52 +0000Mathematics for Natural Science
https://gateoverflow.in/379381/mathematics-for-natural-science
Simplify $(A\cup B)\cap (A\cup B')\cap (A - B)$ for a given non empty sets $A$ and $B$, where $(A\cap B) = \varnothing .$Combinatoryhttps://gateoverflow.in/379381/mathematics-for-natural-scienceFri, 29 Jul 2022 05:20:31 +0000Mathematics for Natural Science
https://gateoverflow.in/379380/mathematics-for-natural-science
Suppose $x, y, z > 1$ are integers, let:<br />
<br />
$p(x,y)$ : $x$ is a factor of $y$<br />
<br />
$q(x,y,z)$ : $z$ = $\text{GCD}(x,y)$<br />
<br />
$r(x)$ : $x$ is prime.<br />
<br />
Check if the following argument is valid or not.<br />
<br />
$(\forall x \exists y)p(x,y) \implies r(x)$ ,<br />
<br />
$(\forall x)(\forall y)(\forall z)(q(x,y,z))$ ,<br />
<br />
$(\exists x)(\forall y)(p(x,y) \lor r(x))$<br />
<br />
$\therefore (\forall y)(\exists z)(\exists x)q(x,y,z)$Mathematical Logichttps://gateoverflow.in/379380/mathematics-for-natural-scienceFri, 29 Jul 2022 05:14:50 +0000Made Easy Test Series
https://gateoverflow.in/379189/made-easy-test-series
<p><img alt="" src="https://gateoverflow.in/?qa=blob&qa_blobid=3134079173675404763"></p>
<p>How to solve this question?</p>Mathematical Logichttps://gateoverflow.in/379189/made-easy-test-seriesSun, 24 Jul 2022 18:04:22 +0000Self Doubt - Planarity of Complete Bipartite Graph
https://gateoverflow.in/378605/self-doubt-planarity-of-complete-bipartite-graph
<p><strong>How to determine for which m, n the complete bipartite graph $Km,n$ is planar?</strong></p>
<p>I am getting two answers from two sources:-</p>
<ol style="list-style-type:decimal" type="1">
<li>A complete bipartite graph $Kmn$ is planar if and only if m<3 or n>3. Source: <a rel="nofollow" href="https://www.javatpoint.com/planar-and-non-planar-graphs#:~:text=A%20complete%20bipartite%20graph%20Kmn%20is%20planar%20if%20and%20only%20if%20m%3C3%20or%20n%3E3.">https://www.javatpoint.com/planar-and-non-planar-graphs#:~:text=A%20complete%20bipartite%20graph%20Kmn%20is%20planar%20if%20and%20only%20if%20m%3C3%20or%20n%3E3.</a></li>
<li>Since $K3,3$ is not planar, but $K2,n$ is planar for every n, we have that Km,n is planar if and only if m ≤ 2 or n ≤ 2. Source: <a rel="nofollow" href="http://www.matthewkahle.org/download/file/fid/573">http://www.matthewkahle.org/download/file/fid/573</a></li>
</ol>
<p>Need a proper proof of the solution. </p>Graph Theoryhttps://gateoverflow.in/378605/self-doubt-planarity-of-complete-bipartite-graphThu, 21 Jul 2022 06:33:51 +0000maths
https://gateoverflow.in/378461/maths
A deck of 5 cards (each carrying a distinct number from 1 to 5) is shuffled thoroughly. Two cards are then removed one at a time from the deck. What is the probability that the two cards are selected with the number on the first card being one higher than the number on the second card ?Probabilityhttps://gateoverflow.in/378461/mathsTue, 19 Jul 2022 14:10:26 +0000Discrete Mathematics and Combinatorics
https://gateoverflow.in/377858/discrete-mathematics-and-combinatorics
Solve the recurrence relation $a^{2}n-5a^{2}_{n-1}+4a^{2} _{n-2}=0$, if $a_{0}=4, a_{1}=13, n>1$Combinatoryhttps://gateoverflow.in/377858/discrete-mathematics-and-combinatoricsFri, 08 Jul 2022 18:50:41 +0000no of solutions to the following inequality 12 <= w + x + y + z <= 14
https://gateoverflow.in/376473/no-of-solutions-to-the-following-inequality-12-w-x-y-z-14
No. of solutions to the following inequality 12 <= w + x + y + z <= 14 where w,x,y,z>=0Combinatoryhttps://gateoverflow.in/376473/no-of-solutions-to-the-following-inequality-12-w-x-y-z-14Wed, 08 Jun 2022 02:05:05 +0000Introduction to Graph Theory Exercises
https://gateoverflow.in/375849/introduction-to-graph-theory-exercises
<p><img alt="" src="https://gateoverflow.in/?qa=blob&qa_blobid=14062839441099743879"></p>
<p>This is the problem snapshot</p>Graph Theoryhttps://gateoverflow.in/375849/introduction-to-graph-theory-exercisesSun, 22 May 2022 07:51:23 +0000A question paper is divided into two parts A and B and each part contains 5 questions. In how many ways a student can answer the question paper, if he has to solve total 6 questions including atleast 2 from each section.
https://gateoverflow.in/375637/question-contains-questions-question-questions-including
I solved the question using the logic first select two questions from each sections. ($\binom{5}{2} * \binom{5}{2}$). Then from remaining 6 questions choose any 2. therefore final ans is = $\binom{5}{2} * \binom{5}{2} * \binom{6}{2}$ which is 1500. Is my answer correct. If wrong What is the mistake. I found this question in an aptitude book which I have. The book mentions the answer as 200.Combinatoryhttps://gateoverflow.in/375637/question-contains-questions-question-questions-includingWed, 18 May 2022 22:57:10 +0000kenneth h rosen chapter 1 section 1.5 PRENEX NORMAL FORM in excercise 1.5
https://gateoverflow.in/374243/kenneth-rosen-chapter-section-prenex-normal-form-excercise
can this topic “PRENEX NORMAL FORM(PNF) ” is necsesary for gate or just i skip this topic.Mathematical Logichttps://gateoverflow.in/374243/kenneth-rosen-chapter-section-prenex-normal-form-excerciseWed, 20 Apr 2022 13:51:59 +0000kenneth h rosen chapter 1 section section 1.5 nested quatnifiers excercise 49
https://gateoverflow.in/374239/kenneth-chapter-section-section-nested-quatnifiers-excercise
49. a) Show that ∀xP (x) ∧ ∃xQ(x) is logically equivalent<br />
to ∀x∃y (P (x) ∧ Q(y)), where all quantifiers have<br />
the same nonempty domain.<br />
b) Show that ∀xP (x) ∨ ∃xQ(x) is equivalent to ∀x∃y<br />
(P (x) ∨ Q(y)), where all quantifiers have the same<br />
nonempty domain.<br />
<br />
<br />
<br />
please anybody tell how to prove this logical equivalency ?Mathematical Logichttps://gateoverflow.in/374239/kenneth-chapter-section-section-nested-quatnifiers-excerciseWed, 20 Apr 2022 12:47:55 +0000kenneth h rosen chapter 1 section 1.5 nested quantifiers excercise 1.5 question 48
https://gateoverflow.in/374222/kenneth-chapter-section-nested-quantifiers-excercise-question
Show that ∀xP (x) ∨ ∀xQ(x) and ∀x∀y(P (x) ∨ Q(y)),<br />
where all quantifiers have the same nonempty domain,<br />
are logically equivalent. (The new variable y is used to<br />
combine the quantifications correctly.)Mathematical Logichttps://gateoverflow.in/374222/kenneth-chapter-section-nested-quantifiers-excercise-questionWed, 20 Apr 2022 06:41:05 +0000kenneth h rosen chapter 1 section nested quantifers excercise 1.5 question 40
https://gateoverflow.in/374213/kenneth-chapter-section-nested-quantifers-excercise-question
Find a counterexample, if possible, to these universally<br />
quantified statements, where the domain for all variables<br />
consists of all integers.<br />
a) ∀x∃y(x = 1/y)<br />
b) ∀x∃y(y^2 − x < 100)Mathematical Logichttps://gateoverflow.in/374213/kenneth-chapter-section-nested-quantifers-excercise-questionTue, 19 Apr 2022 13:48:36 +0000kenneth h rosen chapter 1 section 1.5 nested quantifers question 34
https://gateoverflow.in/374170/kenneth-rosen-chapter-section-nested-quantifers-question
Find a common domain for the variables x, y, and z<br />
for which the statement ∀x∀y((x = y) → ∀z((z = x) ∨<br />
(z = y))) is true and another domain for which it is false.Mathematical Logichttps://gateoverflow.in/374170/kenneth-rosen-chapter-section-nested-quantifers-questionMon, 18 Apr 2022 13:59:48 +0000kenneth h rosen chapter 1 section "Nested quantifers" excercise 1.5 question 26's g
https://gateoverflow.in/374162/kenneth-chapter-section-nested-quantifers-excercise-question
Let Q(x, y) be the statement “x + y = x − y.” If the do-<br />
main for both variables consists of all integers, what are<br />
the truth values?<br />
<br />
g) ∃y∀xQ(x, y)<br />
<br />
Basically i done all the subquestions (a,b,c,d,e,f,h,i) from this question but confused in g subquestion please give answerMathematical Logichttps://gateoverflow.in/374162/kenneth-chapter-section-nested-quantifers-excercise-questionMon, 18 Apr 2022 08:11:57 +0000recurrence relation
https://gateoverflow.in/374110/recurrence-relation
<p><img alt="" src="https://gateoverflow.in/?qa=blob&qa_blobid=10628905654066870099" style="float:right"></p>
<p>T(K)=5T(K-1)-4T(K-2) with initial condition T(0)=2 and T(1)=3 determine T(10).</p>
<p>using recursion i got answer,but can anyone explain above method.</p>
<h1> </h1>
<p> </p>Set Theory & Algebrahttps://gateoverflow.in/374110/recurrence-relationSun, 17 Apr 2022 19:55:39 +0000kenneth h rosen chapter 1 section 1.5 excercise 1.5 question 18 e
https://gateoverflow.in/374082/kenneth-h-rosen-chapter-1-section-1-5-excercise-1-question-18
Express each of these system specifications using predi-<br />
cates, quantifiers, and logical connectives, if necessary.<br />
<br />
<br />
<br />
e) No one knows the password of every user on the sys-<br />
tem except for the system administrator, who knows<br />
all passwords.Mathematical Logichttps://gateoverflow.in/374082/kenneth-h-rosen-chapter-1-section-1-5-excercise-1-question-18Sat, 16 Apr 2022 15:49:21 +0000kenneth h rosen chapter 1 section 1.5 nested quantifiers excercise no 17, b
https://gateoverflow.in/374079/kenneth-rosen-chapter-section-nested-quantifiers-excercise
Express each of these system specifications using predi-<br />
cates, quantifiers, and logical connectives, if necessary.<br />
<br />
b)There is a process that continues to run during all error<br />
conditions only if the kernel is working correctly.Mathematical Logichttps://gateoverflow.in/374079/kenneth-rosen-chapter-section-nested-quantifiers-excerciseSat, 16 Apr 2022 14:22:38 +0000Doubt in By Case Method to check Tautology
https://gateoverflow.in/372967/doubt-in-by-case-method-to-check-tautology
The Truth Value of a compound proposition (if there two pv p,q) is depend on both pv...Then while checking tautology in by case method why we check only one pv’s case like p = true p =false..why we dont check q also?Mathematical Logichttps://gateoverflow.in/372967/doubt-in-by-case-method-to-check-tautologyWed, 23 Mar 2022 23:21:07 +0000kenneth h rosen chapter 1 excercise 1.4 predicates and quantifiers question 46
https://gateoverflow.in/372911/kenneth-chapter-excercise-predicates-quantifiers-question
Exercises 46–49 establish rules for null quantification that<br />
we can use when a quantified variable does not appear in part<br />
of a statement.<br />
46. Establish these logical equivalences, where x does not<br />
occur as a free variable in A. Assume that the domain is<br />
nonempty.<br />
a) (∀xP (x)) ∨ A ≡ ∀x(P (x) ∨ A)<br />
b) (∃xP (x)) ∨ A ≡ ∃x(P (x) ∨ A)<br />
<br />
my doubt is wha is exactly “A” in in this logical expressionsMathematical Logichttps://gateoverflow.in/372911/kenneth-chapter-excercise-predicates-quantifiers-questionSun, 20 Mar 2022 12:30:15 +0000kenneth h rosen chapter 1 excercise 1.4 predicates ad quantifiers question 59 symbolic logic
https://gateoverflow.in/372894/kenneth-excercise-predicates-quantifiers-question-symbolic
Let P (x), Q(x), and R(x) be the statements<br />
<br />
“x is a professor,” “x is ignorant,” and “x is vain,” respectively.<br />
<br />
Express each of these statements using quantifiers; logical connectives; and P (x), Q(x), and R(x), where the<br />
domain consists of all people.<br />
<br />
a) No professors are ignorant.<br />
b) All ignorant people are vain.<br />
c) No professors are vain.<br />
d) Does (c) follow from (a) and (b)<br />
<br />
what is the soution of d) cause i did not understand what the d) says?Mathematical Logichttps://gateoverflow.in/372894/kenneth-excercise-predicates-quantifiers-question-symbolicSat, 19 Mar 2022 12:43:42 +0000kenneth h rosen chapter 1 excercise 1.4 predicates ad quantifiers question 33
https://gateoverflow.in/372890/kenneth-chapter-excercise-predicates-quantifiers-question
Express each of these statements using quantifiers. Then<br />
form the negation of the statement, so that no negation<br />
is to the left of a quantifier. Next, express the negation in<br />
simple English. (Do not simply use the phrase “It is not<br />
the case that.”)<br />
a) Some old dogs can learn new tricks.<br />
b) No rabbit knows calculus.<br />
c) Every bird can fly.<br />
d) There is no dog that can talk.<br />
e) There is no one in this class who knows French and<br />
Russian.Mathematical Logichttps://gateoverflow.in/372890/kenneth-chapter-excercise-predicates-quantifiers-questionSat, 19 Mar 2022 10:40:04 +0000kenneth h rosen excercise 1.4 predicates and quantifiers question 22
https://gateoverflow.in/372874/kenneth-rosen-excercise-predicates-quantifiers-question
<div class="qa-voting-container">
<div class="qa-q-view-stats">
<div class="qa-voting qa-voting-net">
<div class="qa-q-view-content">
<div>22. For each of these statements find a domain for which the<br>
statement is true and a domain for which the statement is<br>
false.<br>
a) Everyone speaks Hindi.<br>
b) There is someone older than 21 years.<br>
c) Every two people have the same first name.<br>
d) Someone knows more than two other people.</div>
</div>
</div>
</div>
</div>Mathematical Logichttps://gateoverflow.in/372874/kenneth-rosen-excercise-predicates-quantifiers-questionFri, 18 Mar 2022 15:49:46 +0000kenneth h rosen chapter 1 excercise 1.3
https://gateoverflow.in/372309/kenneth-h-rosen-chapter-1-excercise-1-3
Show that (p → q) ∧ (q → r) and (p → r) is a logically equivalent to each otherMathematical Logichttps://gateoverflow.in/372309/kenneth-h-rosen-chapter-1-excercise-1-3Tue, 22 Feb 2022 13:40:51 +0000kenneth h rosen chapter 1 excercise 1.3 question 56
https://gateoverflow.in/372279/kenneth-h-rosen-chapter-1-excercise-1-3-question-56
Show that if p, q, and r are compound propositions such<br />
that p and q are logically equivalent and q and r are log-<br />
ically equivalent, then p and r are logically equivalent.Mathematical Logichttps://gateoverflow.in/372279/kenneth-h-rosen-chapter-1-excercise-1-3-question-56Mon, 21 Feb 2022 11:28:45 +0000kenneth h rosen chapter 1 excercise 1.3 question 47
https://gateoverflow.in/372275/kenneth-h-rosen-chapter-1-excercise-1-3-question-47
Show that p NAND q is logically equivalent to ¬(p ∧ q).<br />
<br />
how to prove this and i prove using truth table which is easy but how to prove using logical identities ?<br />
<br />
thank youMathematical Logichttps://gateoverflow.in/372275/kenneth-h-rosen-chapter-1-excercise-1-3-question-47Mon, 21 Feb 2022 09:07:43 +0000Kenneth h rosen chapter 1 excercise 1.3 question 16
https://gateoverflow.in/372271/kenneth-h-rosen-chapter-1-excercise-1-3-question-16
Each of Exercises 16–28 asks you to show that two compound<br />
propositions are logically equivalent. To do this, either show<br />
that both sides are true, or that both sides are false, for exactly<br />
the same combinations of truth values of the propositional<br />
variables in these expressions (whichever is easier).<br />
<br />
<br />
<br />
q16)Show that p ↔ q and (p ∧ q) ∨ (¬p ∧ ¬q) are logically<br />
equivalent.<br />
<br />
so my question is according to above statement how i prove logical equivalence cause i proved using TT and LOgical identities but what is exactly means of this statement<br />
<br />
“ To do this, either show that both sides are true, or that both sides are false, for exactly<br />
the same combinations of truth values of the propositional<br />
variables in these expressions” i didnt understand what statement says<br />
<br />
please tellMathematical Logichttps://gateoverflow.in/372271/kenneth-h-rosen-chapter-1-excercise-1-3-question-16Mon, 21 Feb 2022 07:37:36 +0000Kenneth h rosen chapter 1 excercise 1.2 question 15 on page 23
https://gateoverflow.in/372107/kenneth-h-rosen-chapter-1-excercise-1-2-question-15-on-page-23
Each inhabitant of a remote village always tells the truth or always lies. A villager will give only a “Yes” or a “No” response to a question a tourist asks. Suppose you are a tourist visiting this area and come to a fork in the road. One branch leads to the ruins you want to visit; the other branch leads deep into the jungle. A villager is standing at the fork in the road. What one question can you ask the villager to determine which branch to take?<br />
<br />
<br />
<br />
as answer of this question given in rosen is<br />
<br />
“If I were to ask you whether the right branch leads to the ruins, would you<br />
say 'yes'?”<br />
<br />
<br />
<br />
how this question arise and please explain the reason about this answer to above question<br />
<br />
<br />
<br />
thank youMathematical Logichttps://gateoverflow.in/372107/kenneth-h-rosen-chapter-1-excercise-1-2-question-15-on-page-23Wed, 16 Feb 2022 17:17:56 +0000Kenneth h roesn chapter-1 excercise 1.1 question 23's d) and e) question
https://gateoverflow.in/371390/kenneth-roesn-chapter-excercise-question-23s-and-question
in d. and e. i have a doubt can anyone resolve it ?<br />
<br />
doubt?<br />
<br />
d)It is necessary to walk 8 miles to get to the top of Long’s Peak.<br />
<br />
if we compare with “a necessary condition for p is q“ so i think it would be “p-->q” so it is “if walk 8 miles, then get to top of long’s peak”. if this is not so how it should be “if u get to the top of Long's Peak then then you have to walk 8 miles”.<br />
<br />
E)To get tenure as a professor, it is sufficient to be world-famous.<br />
<br />
if compare with “p is sufficient for q” so here<br />
<br />
p:to get tenure as a professor<br />
<br />
q:to be world famous.<br />
<br />
so it would be p→ q so (if get tenure as professor,then to be world famous)<br />
<br />
<br />
<br />
please resolve this confusion<br />
<br />
thank youMathematical Logichttps://gateoverflow.in/371390/kenneth-roesn-chapter-excercise-question-23s-and-questionSun, 13 Feb 2022 07:45:52 +0000Gate applied test series: Discrete Maths
https://gateoverflow.in/370494/gate-applied-test-series-discrete-maths
<p><img alt="" height="310" src="https://gateoverflow.in/?qa=blob&qa_blobid=7779458018567407876" width="554"></p>
<p>Anyone with detailed solution?</p>Set Theory & Algebrahttps://gateoverflow.in/370494/gate-applied-test-series-discrete-mathsSun, 23 Jan 2022 17:23:36 +0000Discrete Mathematics and Its Applications by Kenneth H. Rosen
https://gateoverflow.in/370436/discrete-mathematics-and-its-applications-by-kenneth-rosen
<p>From where can i get full solution of <strong>Discrete Mathematics and Its Applications by Kenneth H. Rosen</strong> ?</p>Mathematical Logichttps://gateoverflow.in/370436/discrete-mathematics-and-its-applications-by-kenneth-rosenSun, 23 Jan 2022 14:48:36 +0000combinatorics
https://gateoverflow.in/369581/combinatorics
<p>How many 5-digit<strong> even</strong> numbers have <strong>all digits distinct</strong>?</p>Combinatoryhttps://gateoverflow.in/369581/combinatoricsWed, 12 Jan 2022 13:24:16 +0000