GATE Overflow - Recent questions tagged mathematical-logic
http://gateoverflow.in/tag/mathematical-logic
Powered by Question2AnswerDiscrete Maths Kenneth Rosen Nested Quantifiers Ex 1.5 Q8
http://gateoverflow.in/141969/discrete-maths-kenneth-rosen-nested-quantifiers-ex-1-5-q8
<p><em>Let Q(x, y) be the statement “student x has been a contestant
<br>
on quiz show y.” Express each of these sentences
<br>
in terms of Q(x, y), quantifiers, and logical connectives,
<br>
where the domain for x consists of all students at your
<br>
school and for y consists of all quiz shows on television</em>.</p>
<p>
<br>
a) There is a student at your school who has been a contestant
<br>
on a television quiz show.
<br>
b) No student at your school has ever been a contestant
<br>
on a television quiz show.
<br>
c) There is a student at your school who has been a contestant
<br>
on Jeopardy and on Wheel of Fortune.
<br>
d) Every television quiz show has had a student from
<br>
your school as a contestant.
<br>
e) At least two students from your school have been contestants
<br>
on Jeopardy.</p>Mathematical Logichttp://gateoverflow.in/141969/discrete-maths-kenneth-rosen-nested-quantifiers-ex-1-5-q8Sat, 05 Aug 2017 19:07:12 +0000Discrete Mathematics Kenneth H. Rosen Ex 1.4 Predicates and Quantifiers
http://gateoverflow.in/141612/discrete-mathematics-kenneth-rosen-predicates-quantifiers
<p><em>Translate in two ways each of these statements into logical
<br>
expressions using predicates, quantifiers, and logical
<br>
connectives. First, let the domain consist of the students
<br>
in your class and second, let it consist of all people.</em></p>
<p>
<br>
a) Everyone in your class has a cellular phone.
<br>
b) Somebody in your class has seen a foreign movie.
<br>
c) There is a person in your class who cannot swim.
<br>
d) All students in your class can solve quadratic equations.
<br>
e) Some student in your class does not want to be rich</p>Mathematical Logichttp://gateoverflow.in/141612/discrete-mathematics-kenneth-rosen-predicates-quantifiersFri, 04 Aug 2017 11:48:52 +0000Discrete maths Predicate logic
http://gateoverflow.in/140312/discrete-maths-predicate-logic
<ol>
<li>
<p>( ∃x(P(x))→∃x(Q(x)) ) → ( ∃x(P(x)→Q(x)) )</p>
</li>
<li>
<p>( ∃x(P(x)→Q(x)) ) → ( ∃x(P(x))→∃x(Q(x)) )</p>
</li>
</ol>
<p>Which of the above is valid and for not valid please give me counter example where LHS is true but RHS is false?</p>Mathematical Logichttp://gateoverflow.in/140312/discrete-maths-predicate-logicFri, 28 Jul 2017 09:37:05 +0000Two place predicate logic
http://gateoverflow.in/139003/two-place-predicate-logic
How to solve these type of question:-<br />
<br />
∀x ∀y (x+y = 0)<br />
<br />
∀x ∃y (x+y = 0)<br />
<br />
∃x ∀y (x+y = 0)<br />
<br />
∃x ∃y (x+y = 0)<br />
<br />
??Mathematical Logichttp://gateoverflow.in/139003/two-place-predicate-logicFri, 21 Jul 2017 07:27:03 +0000rosen
http://gateoverflow.in/138132/rosen
Show that each of the conditional statement is a tautology<br />
not using truth table<br />
<br />
<br />
<br />
[(p → q) ∧ (q → r)] → (p → r)Mathematical Logichttp://gateoverflow.in/138132/rosenSun, 16 Jul 2017 07:31:06 +0000rosen-eg. 2, section 1.2
http://gateoverflow.in/137983/rosen-eg-2-section-1-2
How can this English sentence be translated into a logical expression?<br />
“You cannot ride the roller coaster if you are under 4 feet tall unless you are older than 16<br />
years old.”<br />
<br />
<br />
<br />
The qustion is given above and the answer in the book is:<br />
(r ∧¬s)→¬q<br />
<br />
<br />
<br />
but what if it was like:<br />
<br />
¬q-->(r ∧¬s)<br />
<br />
<br />
<br />
i mean what if you change the left and right hand sides.Mathematical Logichttp://gateoverflow.in/137983/rosen-eg-2-section-1-2Sat, 15 Jul 2017 10:14:46 +0000Discrete Maths: First Order Logic - Question in my mind based on question from Kenneth Rosen
http://gateoverflow.in/137425/discrete-maths-first-order-logic-question-question-kenneth
<p>This is not a direct question from Rosen but a question that popped up in my head as I was solving problems from Rosen.</p>
<p>1) ∀<sub>x</sub>∃<sub>y</sub>(x≠y → M(x,y))</p>
<p>2) ∀<sub>x</sub>∃<sub>y</sub>(x≠y ∧ M(x,y))</p>
<p>Here the domain of x,y is the students in your class. M(x,y) represents the statement x has sent y an email.</p>
<p>My question is: Are these two statements equivalent or do they mean different things?</p>
<p>Also, could you please explain the difference between the meaning of these statements (in plain English) if they are different?</p>
<p> </p>
<p> </p>Mathematical Logichttp://gateoverflow.in/137425/discrete-maths-first-order-logic-question-question-kennethWed, 12 Jul 2017 10:50:11 +0000Gate Question for CSE 1995 In Propositional logic
http://gateoverflow.in/135004/gate-question-for-cse-1995-in-propositional-logic
<p>I have an question regarding Propositional Logic,</p>
<p><strong>(! = NOT, V = OR, -> = Implication)</strong></p>
<p>If the proposition <strong>!p -> q</strong> is true, then the truth value of the proposition <strong>!p V (p -> q)</strong> is,</p>
<p>1. true 2. multiple valued, 3. false, 4. cannot be determinded</p>
<p>now from the truth table for <strong>!p V (p->q)</strong> i get <strong>1 1 0 1</strong> which means it is neither true nor false.</p>
<p>so the answer would be either 2 or 4 and the actual answer is 4.</p>
<p>My question is what does 'multiple valued' means in this case? is it just there to misdirect or is there any logic behind it? or am i doing this completely wrong?</p>
<p>Please any kind of advice would appreciated!!!</p>Mathematical Logichttp://gateoverflow.in/135004/gate-question-for-cse-1995-in-propositional-logicTue, 27 Jun 2017 19:51:58 +0000[Discrete Maths] predicate Logic
http://gateoverflow.in/133755/discrete-maths-predicate-logic
<pre>
<code>Represent using logic connectives :-
1. "Whenever there is an active alert, all queued messages are transmitted."</code></pre>
<p>Given answer is :-∃x(Alert(x)∧Active(x))→∀y((Message(y)∧Queued(y))→Transmitted(y))</p>
<p>2. Purple mushrooms are poisonous</p>
<p>∀x( purple(x)∧mushroom(x)→ Poisonous(x) )</p>
<p>I need to ask that in first statement why are we using ∃x instead of ∀ in the beginning . I mean it should be same as If there is an active alert then do XYZ.Like in second statement. If i use ∀ in the begriming then it will become "For every object x in universe if x is an active alert then queued messages are transmitted". What is wrong in this?</p>
<p>so ∀(Alert(x) ^ Active(x) -> XYZ).</p>
<p>Why are we using ∃ in the start.?</p>Mathematical Logichttp://gateoverflow.in/133755/discrete-maths-predicate-logicSun, 18 Jun 2017 19:47:44 +0000[Discrete Maths] First Order Logic
http://gateoverflow.in/133130/discrete-maths-first-order-logic
<p><img alt="" src="http://gateoverflow.in/?qa=blob&qa_blobid=9721698226079299898"></p>Mathematical Logichttp://gateoverflow.in/133130/discrete-maths-first-order-logicThu, 15 Jun 2017 04:38:15 +0000[Discrete Maths] predicate Logic
http://gateoverflow.in/133129/discrete-maths-predicate-logic
<p><img alt="" src="http://gateoverflow.in/?qa=blob&qa_blobid=9721698226079299898"></p>Mathematical Logichttp://gateoverflow.in/133129/discrete-maths-predicate-logicThu, 15 Jun 2017 04:37:42 +0000[Discrete Maths] predicate logic
http://gateoverflow.in/132949/discrete-maths-predicate-logic
<p>Whether following statement is correct?</p>
<blockquote>
<p>Every satisfiable is not tautology.</p>
</blockquote>
<p>I am reading it as:-</p>
<p>1st way :- If it is satisfiable then it is not tautology. So it should be false</p>
<p>2nd way:- It is same as saying that every satisfiable is not tautology because there are some satisfiable which are not tautologies as they are contingencies.</p>
<p>Please clarify which is correct and why?</p>
<p> </p>
<p> </p>Mathematical Logichttp://gateoverflow.in/132949/discrete-maths-predicate-logicWed, 14 Jun 2017 02:08:11 +0000first order logic notations
http://gateoverflow.in/132898/first-order-logic-notations
can someone please tell when to interpret this symbol $\Leftrightarrow$ as logical equivalence and when as double implication?Mathematical Logichttp://gateoverflow.in/132898/first-order-logic-notationsTue, 13 Jun 2017 11:18:23 +0000FREE VARIABLE and VALIDITY related problem
http://gateoverflow.in/132789/free-variable-and-validity-related-problem
<p>Given that </p>
<h2><strong>LHS : </strong><strong>[(∃x,α(x))→β]</strong>
<br>
<strong>RHS</strong> : <strong>[∃x,α(x)→β]</strong></h2>
<p><strong>Here α(x) is a first order formula with x as a free variable, and β is a first order formula with no free variable.</strong></p>
<p>than which one is valid ?</p>
<h3>a) <strong>LHS → RHS</strong></h3>
<h3>b) <strong>RHS → LHS</strong></h3>Mathematical Logichttp://gateoverflow.in/132789/free-variable-and-validity-related-problemMon, 12 Jun 2017 15:05:11 +0000# FREE VARIABLE ( NULL QUANTIFICATION ) Related problem
http://gateoverflow.in/132788/%23-free-variable-null-quantification-related-problem
<h2>Given that </h2>
<h2><strong>LHS : [(∃</strong><strong>x,α(x))→β]</strong></h2>
<h2><strong>RHS : [∃x,α(x)→β]</strong></h2>
<p> </p>
<p>than which one is valid ?</p>
<p>a) <strong>LHS</strong> <strong>→ RHS</strong></p>
<p>b) <strong>RHS → LHS</strong></p>Mathematical Logichttp://gateoverflow.in/132788/%23-free-variable-null-quantification-related-problemMon, 12 Jun 2017 15:00:44 +0000ISI 2017 MMA
http://gateoverflow.in/132734/isi-2017-mma
The area lying in the first quadrant and bounded by the circle<br />
<br />
x^2 + y^2 = 4<br />
<br />
and lines <br />
<br />
x=0 and x=1<br />
<br />
is given by?Numerical Abilityhttp://gateoverflow.in/132734/isi-2017-mmaMon, 12 Jun 2017 06:46:09 +0000Mathematical Logic
http://gateoverflow.in/132576/mathematical-logic
<p>What is the difference between =>, <=> and ->?</p>
<p>Are => and -> used in the same way? => is logical implication and <=> is equivalence right? Then why does in some questions, => and <=> is read as 'if then'? '->' symbol is for if then right?</p>
<p>Refer to this: <a rel="nofollow" href="http://gateoverflow.in/3454/gate2007-it-21">http://gateoverflow.in/3454/gate2007-it-21</a></p>Mathematical Logichttp://gateoverflow.in/132576/mathematical-logicSat, 10 Jun 2017 16:22:47 +0000[Discrete Maths] Predicate Logic,Rosen Ex1.5,problem,9.e
http://gateoverflow.in/132448/discrete-maths-predicate-logic-rosen-ex1-5-problem-9-e
<table>
<tbody>
<tr>
<td>
<p> </p>
</td>
<td>
<p><strong>Q</strong>: Consider the following premises:-</p>
<p>1.1. What is good for corporations is good for the United States.
<br>
2.2. What is good for the United States is good for you.
<br>
3.3. What is good for the corporations is for you to buy lots of stuff.</p>
<p>What are the valid conclusions?</p>
</td>
</tr>
</tbody>
</table>Mathematical Logichttp://gateoverflow.in/132448/discrete-maths-predicate-logic-rosen-ex1-5-problem-9-eFri, 09 Jun 2017 17:50:27 +0000[Discrete Maths] Predicate logic
http://gateoverflow.in/132433/discrete-maths-predicate-logic
Are the following statements same?<br />
<br />
1. Everybody loves exactly one person.<br />
<br />
2.There is exactly one person whom everybody lovesMathematical Logichttp://gateoverflow.in/132433/discrete-maths-predicate-logicFri, 09 Jun 2017 15:21:00 +0000gatebook predicate logic practice problems
http://gateoverflow.in/132195/gatebook-predicate-logic-practice-problems
Hi Can anyone please explain this statements<br />
<br />
S1: ∀x ∃y ∀z [ x+ y = z]<br />
<br />
S2: ∃x ∀y ∃z [x + y = z]<br />
<br />
Where x, y, z are real numbers. Which of the following statement is true?Mathematical Logichttp://gateoverflow.in/132195/gatebook-predicate-logic-practice-problemsWed, 07 Jun 2017 08:10:30 +0000Gatebook - predicate Logic - negating
http://gateoverflow.in/132090/gatebook-predicate-logic-negating
PFB practice question from GATEBOOK on predicate logic.<br />
<br />
a) Everyone loves every one<br />
<br />
Solution: somebody hates somebody<br />
<br />
b) Nobody loves everybody<br />
<br />
Solution: someone loves every body<br />
<br />
c) Somebody loves somebody<br />
<br />
Solution: nobody loves somebody<br />
<br />
d) Everyone loves some one<br />
<br />
Solution: somebody loves nobody.<br />
<br />
is below are correct for the above statements:<br />
<br />
a)No one Loves Everyone<br />
<br />
b)Everybody Loves Everybody<br />
c)everybody loves everybody<br />
<br />
d)Nobody Loves SomeoneMathematical Logichttp://gateoverflow.in/132090/gatebook-predicate-logic-negatingTue, 06 Jun 2017 12:23:51 +0000first order logic
http://gateoverflow.in/132011/first-order-logic
Is it always the case that implication comes with universal quantifier and conjunction comes with existential quantifier?Mathematical Logichttp://gateoverflow.in/132011/first-order-logicMon, 05 Jun 2017 17:23:35 +0000#general #mathematics #PropositionalLogic How to Choose which one is better answer?
http://gateoverflow.in/131744/%23general-%23mathematics-%23propositionallogic-choose-better
How to Choose which one is a better answer and which is ideally good answer in propositional logic?<br />
<br />
<br />
<br />
let me tell you the context. Let's take an example.<br />
<br />
<br />
<br />
Use quantifiers and predicates with more than one variable to express these statements.<br />
<br />
a) Every computer science student needs a course in Discrete Mathematics.<br />
<br />
now there is various possible solution for this statement but following the same logic.<br />
<br />
solution 1) if the domain is all the people world, S(x) means x is a student of this school, CS(x) x Is in Computer Science class, DM(x) x takes DM course.<br />
<br />
$\forall \left ( S(x)\wedge CS(x)\rightarrow DM(x) \right )$<br />
<br />
solution 2) $\forall \left ( P(x) \right )$<br />
<br />
where P(x), x needs a course in DM and domain consist of all computer science student.<br />
<br />
<br />
<br />
just by changing domain "in words" the scenario changed here. then how to choose the limit of domain and flexibility of it. How to choose which is one is better?Mathematical Logichttp://gateoverflow.in/131744/%23general-%23mathematics-%23propositionallogic-choose-betterSat, 03 Jun 2017 12:00:36 +0000This problem is related to Rule of inference and valid argument .
http://gateoverflow.in/131660/this-problem-is-related-to-rule-inference-and-valid-argument
premises are -<br />
<br />
A<br />
<br />
A → ( B ∨ C )<br />
<br />
B → ¬A<br />
<br />
conclusion -<br />
<br />
C<br />
<br />
<br />
<br />
is valid or not ?Mathematical Logichttp://gateoverflow.in/131660/this-problem-is-related-to-rule-inference-and-valid-argumentFri, 02 Jun 2017 17:59:48 +0000Predicate Logic For All Quantifier
http://gateoverflow.in/131657/predicate-logic-for-all-quantifier
"Every Lion Drinks Coffee'.<br />
<br />
UoD : Animals<br />
<br />
The equivalent First Order Logic statement for the above statment is<br />
<br />
$\forall x(Cat(x) )\rightarrow Coffee(x))$<br />
<br />
Lets consider in UoD (animals), let there may be a CAT, TIGER ..etc and consider below statment<br />
<br />
Tiger Drinks Coffee. then the first order logic statment<br />
$\forall x(F \rightarrow T)$<br />
<br />
this statement also satisfying and giving the truth value.<br />
<br />
But our actual statement is 'Every Lion Drinks Coffee' right??<br />
<br />
I think the statement ' Every Lion Drinks Coffee', doesn't mean, if an animal is not a lion, then it shouldn't drink coffee??. if its true then the first order logic statement is valid.Mathematical Logichttp://gateoverflow.in/131657/predicate-logic-for-all-quantifierFri, 02 Jun 2017 17:48:18 +0000[Discrete Maths] Predicate Logic):-
http://gateoverflow.in/131655/discrete-maths-predicate-logic
A(x) :- Apple on the table.<br />
<br />
Give predicate logic that there is at most one apple on the table.<br />
<br />
1. ∃x∃y(A(x) ^ A(y) ) ->x=y<br />
<br />
2.∀x∀y(A(x) ^ A(y) ) ->x=y<br />
<br />
I know first one is correct,but why second one is not correct?<br />
<br />
If i translate first:- If there exists two apples then they must be same.And if LHS is false,i.e there is no apple then RHS will be true.So it fits both cases of 0 and 1 apple<br />
<br />
If i translate second:- If any two objects in the universe are apples on the table ,then they must be same.It also follows same thing.<br />
<br />
So are both versions correct?Or i am mistaking somehwere?Mathematical Logichttp://gateoverflow.in/131655/discrete-maths-predicate-logicFri, 02 Jun 2017 17:46:33 +0000Kenneth Rosen
http://gateoverflow.in/131575/kenneth-rosen
Show that the following statement is a tautology using Truth Table<br />
<br />
( p ^ q) --> p <br />
<br />
I have some minor doubts in this seemingly simple question.<br />
<br />
First a tautology is a statement which is always True, but while solving the question we get 1 False value, so how is still called a tautology?Mathematical Logichttp://gateoverflow.in/131575/kenneth-rosenFri, 02 Jun 2017 06:13:40 +0000rosen-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 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 +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/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 +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/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 +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 +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 />
<br />
"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 />
<br />
Answer was given as :<br />
<br />
(∃x F(x,10))→∃x S(x)<br />
<br />
Where F(x,y) Disk x has more than y kilobytes of free space<br />
<br />
S(x) Mail message x can be saved.<br />
<br />
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 />
<br />
What is meant by the below expression?<br />
<br />
∀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 +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 />
<br />
q:"you can ride roller coaster"<br />
r:"you are under 4 feet tall"<br />
s:"you are older than 16"<br />
<br />
For representing" you cannot ride the roller coaster if you are under 4 feet tall unless you are older than 16 years old"<br />
<br />
(-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 />
<br />
Now, which is correct?Mathematical Logichttp://gateoverflow.in/126009/chapter-1-kenneth-rosen-page-17-eg-2Mon, 17 Apr 2017 22:59:35 +0000First Order Logic
http://gateoverflow.in/124596/first-order-logic
Can some explain the basics of First Order Logic like what various terms means, what are various properties ?Study Resourceshttp://gateoverflow.in/124596/first-order-logicFri, 07 Apr 2017 12:14:08 +0000logic
http://gateoverflow.in/124485/logic
<p>can somebody explain the intution behind this ...? i am not able to get ....and i dont want to by-heart ....<img alt="" src="http://gateoverflow.in/?qa=blob&qa_blobid=16599048480255075131"></p>Mathematical Logichttp://gateoverflow.in/124485/logicThu, 06 Apr 2017 19:49:49 +0000Conjunction of Disjunction
http://gateoverflow.in/124066/conjunction-of-disjunction
Can anyone please explain conjuction of disjunction rule in converting PL to CNF?<br />
<br />
<br />
<br />
Thank you!Mathematical Logichttp://gateoverflow.in/124066/conjunction-of-disjunctionTue, 04 Apr 2017 21:31:42 +0000Kenneth H. Rosen
http://gateoverflow.in/123803/kenneth-h-rosen
<p> Let <em>C(x) </em>be the statement <em>"x </em>has a cat;' let <em>D(x) </em>be the statement "x has a dog," and let <em>F(x) </em>be the statement "x has a ferret:' Express each of these statements in terms of <em>C(x), </em>D(x), <em>F(x), </em>quantifiers, and logical connectives. Let the domain consist of all students in your class.</p>
<ol style="list-style-type:lower-alpha">
<li>A student in your class has a cat, a dog, and a ferret.</li>
<li>All students in your class have a cat, a dog, or a ferret.</li>
<li>Some student in your class has a cat and a ferret, but not a dog.</li>
<li>No student in your class has a cat, a dog, and a ferret.</li>
<li>For each of the three animals, cats, dogs, and ferrets, • there is a student in your class who has this animal as a pet.</li>
</ol>Mathematical Logichttp://gateoverflow.in/123803/kenneth-h-rosenMon, 03 Apr 2017 20:52:11 +0000logic
http://gateoverflow.in/123124/logic
<p><img alt="" src="http://gateoverflow.in/?qa=blob&qa_blobid=3341390517395662876"></p>
<p><strong>Is there anyother way to solve this problem other than drawing the complete truth table ?</strong></p>Mathematical Logichttp://gateoverflow.in/123124/logicFri, 31 Mar 2017 17:23:01 +0000propositional logic
http://gateoverflow.in/120835/propositional-logic
Which of the following statements are ALWAYS TRUE ?<br />
<br />
A) ∀x [P(x)] ---> ∃x [P(x)]<br />
<br />
B) ∃x [P(x)] ---> ∀x [P(x)]<br />
<br />
C) Both A) and B) and so both are equivalent <br />
<br />
D) Neither A) nor B)Mathematical Logichttp://gateoverflow.in/120835/propositional-logicTue, 07 Mar 2017 19:29:38 +0000propositional logic
http://gateoverflow.in/120826/propositional-logic
Which of the following propositional statements is TRUE ?<br />
<br />
A) ∀x ∀z ∃y [ P(x,y) ]---> ∃y ∀x ∀z [ P(x,y) ]<br />
<br />
B) ∃y ∀x ∀z [ P(x,y) ]---> ∀x ∀z ∃y [ P(x,y) ]<br />
<br />
C) Both A) and B) and so both are equivalent <br />
<br />
D) None of the above.Mathematical Logichttp://gateoverflow.in/120826/propositional-logicTue, 07 Mar 2017 17:47:07 +0000propositional logic
http://gateoverflow.in/120759/propositional-logic
Translate each of these statements into logical expressions<br />
<br />
a) Someone in your school has visited Uzbekistan.<br />
b) Everyone in your class has studied calculus and C++.<br />
c) No one in your school owns both a bicycle and a motorcycle.<br />
d) There is a person in your school who is not happy.<br />
e) Everyone in your school was born in the twentieth<br />
century.Mathematical Logichttp://gateoverflow.in/120759/propositional-logicTue, 07 Mar 2017 11:37:39 +0000propositional logic
http://gateoverflow.in/120748/propositional-logic
<p>Convert into logical expression </p>
<p><em><strong>"Not everybody in the school is perfect"</strong></em></p>
<p>A) NOT( ∀x(S(x)--->P(x) )</p>
<p>B) ∃x( S(x) ^ NOT (P(x)) )</p>
<p>C) Either A) or B)</p>
<p>D) None of the above </p>
<p> </p>Mathematical Logichttp://gateoverflow.in/120748/propositional-logicTue, 07 Mar 2017 10:12:16 +0000propositional logic
http://gateoverflow.in/120744/propositional-logic
<p>Translate the statement into logical expression</p>
<p><em><strong>"Not everybody is your friend or someone is not perfect"</strong></em></p>
<p> </p>Mathematical Logichttp://gateoverflow.in/120744/propositional-logicTue, 07 Mar 2017 09:10:01 +0000