GATE Overflow - Recent questions in Mathematical Logic
http://gateoverflow.in/questions/mathematics/discrete-mathematics/mathematical-logic
Powered by Question2AnswerProbability
http://gateoverflow.in/134654/probability
P( A union B)=.6<br />
<br />
P( A intersection B)=.25<br />
<br />
Find P(A`) +P(B`) ? <br />
<br />
where P(A`) means probability of A complement.Mathematical Logichttp://gateoverflow.in/134654/probabilitySat, 24 Jun 2017 20:57:59 +0000Rosen
http://gateoverflow.in/133952/rosen
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 years old.”Mathematical Logichttp://gateoverflow.in/133952/rosenTue, 20 Jun 2017 03:10:53 +0000Diameter of a graph and tree
http://gateoverflow.in/133949/diameter-of-a-graph-and-tree
Why there is a difference between diameter of a graph and tree?<br />
<br />
Diameter of a tree as i have read is the maximum path between two vertices(number of edges between two vertices)<br />
<br />
But for tree it says number of nodes on the longest path.<br />
<br />
But tree is a graph so why cant i find the diameter of tree in similar way?Mathematical Logichttp://gateoverflow.in/133949/diameter-of-a-graph-and-treeTue, 20 Jun 2017 01:43:39 +0000[Discrete Maths] Generating functions
http://gateoverflow.in/133773/discrete-maths-generating-functions
<p><img alt="" src="http://gateoverflow.in/?qa=blob&qa_blobid=11849429701953093316"></p>Mathematical Logichttp://gateoverflow.in/133773/discrete-maths-generating-functionsMon, 19 Jun 2017 02:10:59 +0000[Discrete maths] Exponent generating function
http://gateoverflow.in/133771/discrete-maths-exponent-generating-function
<p><img alt="" src="http://gateoverflow.in/?qa=blob&qa_blobid=17007664129300006410"></p>
<p>Please tell how to solve d and e?</p>Mathematical Logichttp://gateoverflow.in/133771/discrete-maths-exponent-generating-functionMon, 19 Jun 2017 02:09:04 +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 +0000Testbook test series
http://gateoverflow.in/133514/testbook-test-series
<p><img alt="" height="175" src="http://gateoverflow.in/?qa=blob&qa_blobid=14500814523810473119" width="280"></p>Mathematical Logichttp://gateoverflow.in/133514/testbook-test-seriesSat, 17 Jun 2017 06:21:32 +0000Testbook testseries
http://gateoverflow.in/133513/testbook-testseries
<p><img alt="" height="175" src="http://gateoverflow.in/?qa=blob&qa_blobid=11022826522543751454" width="300"></p>Mathematical Logichttp://gateoverflow.in/133513/testbook-testseriesSat, 17 Jun 2017 06:18:50 +0000[Self doubt] Permutation
http://gateoverflow.in/133489/self-doubt-permutation
Default permutation is with repetition or not?I came across some questions and it was nothing mentioned like repetition and all.But if questions says how many passwords then it was assumed that they are distinct and repetition not allowed and some questions asks like how many licenses number possible where 1 letter followed by 4 digits etc. and in these question it was with repitiion.So how to differentiate between these two?Mathematical Logichttp://gateoverflow.in/133489/self-doubt-permutationSat, 17 Jun 2017 00:10:37 +0000Rosen #MATHEMATICAL LOGIC
http://gateoverflow.in/133441/rosen-%23mathematical-logic
Chapter 1 Exercise1.4 question 9.h<br />
<br />
Let L(x, y) be the statement "x loves y" where the domain of x and y consist of all people of the world. Use quantifiers to expess the statement :<br />
<br />
"THERE ARE EXACTLY TWO PEOPLE WHOM LYNN LOVES"Mathematical Logichttp://gateoverflow.in/133441/rosen-%23mathematical-logicFri, 16 Jun 2017 16:24:31 +0000[Discrete Maths] Group Theory
http://gateoverflow.in/133264/discrete-maths-group-theory
If the group has 40 elements and it has two subgroups namely h and k with order 10 and 20 then what can't be order of (h intersection k)<br />
<br />
a:)10<br />
<br />
b:)20<br />
<br />
c:)3<br />
<br />
d:)1<br />
<br />
e:) 4<br />
<br />
My answer is both c and b and e. Is it correct?Mathematical Logichttp://gateoverflow.in/133264/discrete-maths-group-theoryThu, 15 Jun 2017 15:26:18 +0000[Discrete Maths] Dual of a function
http://gateoverflow.in/133131/discrete-maths-dual-of-a-function
<p><img alt="" src="http://gateoverflow.in/?qa=blob&qa_blobid=16891012436546364258"></p>Mathematical Logichttp://gateoverflow.in/133131/discrete-maths-dual-of-a-functionThu, 15 Jun 2017 04:39:42 +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 +0000Counting
http://gateoverflow.in/132945/counting
How many ways are there to put six temporary employees into four labeled offices so that there is at least one temporary employee in each of these four offices?Mathematical Logichttp://gateoverflow.in/132945/countingWed, 14 Jun 2017 00:21:55 +0000[Discrete maths ] Group theory
http://gateoverflow.in/132942/discrete-maths-group-theory
<p>Let G be abelian, H and K subgroups of G with orders n, m. Then G has subgroup of order lcm(n,m)</p>
<p>I have gone through prrof here:- <a rel="nofollow" href="https://math.stackexchange.com/questions/465742/let-g-be-abelian-h-and-k-subgroups-of-orders-n-m-then-g-has-subgrou">https://math.stackexchange.com/questions/465742/let-g-be-abelian-h-and-k-subgroups-of-orders-n-m-then-g-has-subgrou</a></p>
<p>But this uses assertion :- if G is abelian and n divides |G| then G has a subgroup of order n.How is this assertion true. there are some existing examples where n divides G but there is no subgroup with that order.Please clear with explanation.</p>
<p> </p>Mathematical Logichttp://gateoverflow.in/132942/discrete-maths-group-theoryTue, 13 Jun 2017 22:18:33 +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 +0000[Discrete Maths] Graph Theory Rosen,Chromatic number
http://gateoverflow.in/132851/discrete-maths-graph-theory-rosen-chromatic-number
<p>What are the chromatic number of following graphs?</p>
<p> </p>
<p><img alt="" src="http://gateoverflow.in/?qa=blob&qa_blobid=2427432278983743495"></p>
<p>Answer is 6 and 4 respectively.But i am getting 3 for both.</p>
<p>Please someone confirm this?</p>Mathematical Logichttp://gateoverflow.in/132851/discrete-maths-graph-theory-rosen-chromatic-numberTue, 13 Jun 2017 03:38:59 +0000[Discrete Maths] Hamilton Circuit,Rosen p-584,q47
http://gateoverflow.in/132840/discrete-maths-hamilton-circuit-rosen-p-584-q47
<p>How is the following graph is Hamilton?The answer says it has Hamilton circuit</p>
<p>.<img alt="" src="http://gateoverflow.in/?qa=blob&qa_blobid=8250483095399749125"> </p>Mathematical Logichttp://gateoverflow.in/132840/discrete-maths-hamilton-circuit-rosen-p-584-q47Tue, 13 Jun 2017 02:12:09 +0000Discrete Maths Graph theory
http://gateoverflow.in/132838/discrete-maths-graph-theory
What are the necessary and sufficient conditions for Euler path and Circuit in directed graph?Mathematical Logichttp://gateoverflow.in/132838/discrete-maths-graph-theoryTue, 13 Jun 2017 01:37:24 +0000Discrete maths equivalence relation
http://gateoverflow.in/132834/discrete-maths-equivalence-relation
Consider the equivalence relation<br />
namely, R = (x, y) I x - y is an integer}.<br />
<br />
What is the equivalence class of R={ (x,y) | x-y in integer(Z)} equivalence<br />
relation?<br />
<br />
Given answer is :- (n + 1/2 I n E Z)<br />
<br />
My answer is :- (n*1/2 | n E Z)<br />
<br />
<br />
<br />
Is my answer correct also?Mathematical Logichttp://gateoverflow.in/132834/discrete-maths-equivalence-relationMon, 12 Jun 2017 20:41:16 +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 +0000[Discrete Maths] Inclusion/Exclusion Probability
http://gateoverflow.in/132699/discrete-maths-inclusion-exclusion-probability
find the probability that when four numbers from 1 to 100,inclusive,are picked at random with no repetitions allowed,either all are odd,all divisible by 3,or all divisible by 5Mathematical Logichttp://gateoverflow.in/132699/discrete-maths-inclusion-exclusion-probabilitySun, 11 Jun 2017 17:56:46 +0000#rosen_chapter1
http://gateoverflow.in/132684/%23rosen_chapter1
<p>1.49. The <em>n</em>th statement in a list of 100 statements is “Exactly <em>n </em>of the statements in this list are false.”
<br>
a) What conclusions can you draw from these statements?
<br>
b) Answer part (a) if the <em>n</em>th statement is “At least <em>n </em>of the statements in this list are false.”
<br>
c) Answer part (b) assuming that the list contains 99 statements</p>
<p>explain this </p>Mathematical Logichttp://gateoverflow.in/132684/%23rosen_chapter1Sun, 11 Jun 2017 15:58:09 +0000#rosen_chapter1
http://gateoverflow.in/132683/%23rosen_chapter1
<p>(1.15) Let <em>p</em>, <em>q</em>, and <em>r </em>be the propositions
<br>
<em>p </em>: Grizzly bears have been seen in the area.
<br>
<em>q </em>: Hiking is safe on the trail.
<br>
<em>r </em>: Berries are ripe along the trail</p>
<p>Write below using propositions logic</p>
<p>c) “If berries are ripe along the trail, hiking is safe if and only if grizzly bears have not been seen in the area” is written as ((r->q)<->-p becoz -> has higher precedence then <-></p>
<p>e)” For hiking on the trail to be safe, it is necessary but not sufficient that berries not be ripe along the trail and for grizzly bears not to have been seen in the area” is written as ((q->(-r^-p)^-((-r^-p)->q))</p>
<p>verify this </p>Mathematical Logichttp://gateoverflow.in/132683/%23rosen_chapter1Sun, 11 Jun 2017 15:56:29 +0000#rosen_chapter1
http://gateoverflow.in/132682/%23rosen_chapter1
<p>(1.13.f) Let <em>p </em>and <em>q </em>be the propositions
<br>
p: You drive over 65 miles per hour.
<br>
Q: You get a speeding ticket.</p>
<p>This statement “ You get a speeding ticket, but you do not drive over 65 miles per hour” is written as (q^-p) in proposition logic</p>
<p>Verify this </p>Mathematical Logichttp://gateoverflow.in/132682/%23rosen_chapter1Sun, 11 Jun 2017 15:54:41 +0000[Discrete maths] Generating function
http://gateoverflow.in/132616/discrete-maths-generating-function
9. Find the coefficient of x lO in the power series of each of<br />
these functions.<br />
a. (x^2 +x^4 +x^6 +x^8 + .. . )(x^3 +x^6 +x^9 + .. ·)(x^4 +<br />
x^8 +X^12 + ... )<br />
b. (I +x^2+x^4+x^6+ x^8+ ... )(1 +x^4+X^8+X^I2 + ... )<br />
(I +x^6 +x^12 +x^18 + ... )Mathematical Logichttp://gateoverflow.in/132616/discrete-maths-generating-functionSun, 11 Jun 2017 04:26:43 +0000[Discrete maths] Permutations and combinations
http://gateoverflow.in/132599/discrete-maths-permutations-and-combinations
<pre>
How many ways can n books be placed on k distinguishable shelves
a. if no two books are the same ,and the positions of the books on the shelves does not matter?
b. if no two books are the same,and the positions of the books on the shelves matter?
</pre>Mathematical Logichttp://gateoverflow.in/132599/discrete-maths-permutations-and-combinationsSat, 10 Jun 2017 20:38:11 +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 ] Counting
http://gateoverflow.in/132567/discrete-maths-counting
One hundred tickets numbered from 1 to 100 are sold to 100 different people for a drawing. Four different prizes are to be awarded including the Grand Prize (a trip to Tahiti).<br />
<br />
1) How many ways are there to award the prizes?<br />
<br />
2) How many ways are there to award the prizes if the person holding ticket #47 wins the Grand Prize?<br />
<br />
3) How many ways are there to award the prizes if the person holding ticket #47 wins one of the prizes?<br />
<br />
4) How many ways are there to award the prizes if the person holding ticket #47 does not win a prize?<br />
<br />
I need to clarification on 4th part.I solved it as (Answer for 1- Answer for 3) but it doesn't give the right answer.What did i miss?Mathematical Logichttp://gateoverflow.in/132567/discrete-maths-countingSat, 10 Jun 2017 14:51:30 +0000[Discrete maths] permutations
http://gateoverflow.in/132560/discrete-maths-permutations
How many possibilities are there for the win, place and show (first, second, and third) positions in a horse race with 12 horses if all orders of finish are possible?Mathematical Logichttp://gateoverflow.in/132560/discrete-maths-permutationsSat, 10 Jun 2017 13:52:00 +0000[Discrete Maths] Function,Rosen p-154.1.c
http://gateoverflow.in/132557/discrete-maths-function-rosen-p-154-1-c
<p>Does the following represents function from R->R ?</p>
<p> </p>
<p>f(x)=√x</p>
<p>In ths solution ,it is given:- f(x) is not defined for x < O. </p>
<p>But do we consider it by default as +/-√x or is it only +√x?</p>
<p>I have asked a similar ques:-<a rel="nofollow" href="http://gateoverflow.in/132553/discrete-maths-group-theory">http://gateoverflow.in/132553/discrete-maths-group-theory</a></p>Mathematical Logichttp://gateoverflow.in/132557/discrete-maths-function-rosen-p-154-1-cSat, 10 Jun 2017 13:39:16 +0000[Discrete maths] Group Theory
http://gateoverflow.in/132553/discrete-maths-group-theory
Can the following operation be used with a non empty set to represent a group?<br />
a*b=sqrt($a^{2}+b^{2}$)<br />
<br />
My doubt is,does this operation represents a function or do we include +- sign both as output ?Mathematical Logichttp://gateoverflow.in/132553/discrete-maths-group-theorySat, 10 Jun 2017 13:19:41 +0000[Discrete Maths] Counting
http://gateoverflow.in/132473/discrete-maths-counting
In how many ways can a photographer at a wedding arrange six people in a row, including the bride and groom, if the bride is positioned somewhere to the left of the groom?<br />
<br />
Please suggest non brute force approachMathematical Logichttp://gateoverflow.in/132473/discrete-maths-countingSat, 10 Jun 2017 01:28:04 +0000[Discrete maths] Rosen p-154,functions,7.b
http://gateoverflow.in/132471/discrete-maths-rosen-p-154-functions-7-b
Find range and domain:-<br />
<br />
The function that assigns to each positive integer the number of the digits 0,1,2,3,4,5,6,7,8,9 that do not appear as digits in the decimal representation of the integerMathematical Logichttp://gateoverflow.in/132471/discrete-maths-rosen-p-154-functions-7-bFri, 09 Jun 2017 20:53:22 +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 +0000[Discrete Maths] Rosen,p-46,41.b
http://gateoverflow.in/132366/discrete-maths-rosen-p-46-41-b
Express using predicate,quantifies and connectives:-<br />
<br />
The diagnostic monitor tracks status of all systems except main consoleMathematical Logichttp://gateoverflow.in/132366/discrete-maths-rosen-p-46-41-bFri, 09 Jun 2017 02:36:58 +0000[Discrete maths] graph theory Perfect matching
http://gateoverflow.in/132353/discrete-maths-graph-theory-perfect-matching
When matching number and covering number are same then can we say that it is a perfect matching case?Do i need to check the elements of the set( edges in both matching and covering) also if their cardinality is same?If yes,then can someone give me an example where matching number and covering number same but still it is not a perfect match?I am not able to find such a case and i think it will not exist.Mathematical Logichttp://gateoverflow.in/132353/discrete-maths-graph-theory-perfect-matchingThu, 08 Jun 2017 20:41:26 +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 +0000Propositional Logic
http://gateoverflow.in/132140/propositional-logic
#Discrete_Maths<br />
#Logic<br />
<br />
I have a doubt in the following concept.<br />
Suppose we're given:<br />
(A v B) ^ ( B v C)...when we open the brackets, do we apply distributive law or just open it..as in<br />
1. A v B ^ B v C = A v B ^ C<br />
2. ((A v B) ^ B) v ((A v B) ^ C) ( by distributive law)<br />
<br />
Which one of the above is correct and why? Also, when exactly do we apply distributive law? I see that sometimes, the brackets are opened just like that and in other cases, distributive law is used. How to differentiate what to do when?<br />
<br />
Please help!Mathematical Logichttp://gateoverflow.in/132140/propositional-logicTue, 06 Jun 2017 23:25:40 +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#PropositionLogic #rossen
http://gateoverflow.in/131789/%23propositionlogic-%23rossen
49. The nth statement in a list of 100 statements is “Exactly<br />
n of the statements in this list are false.”<br />
a) What conclusions can you draw from these statements?<br />
b) Answer part (a) if the nth statement is “At least n of<br />
the statements in this list are false.”<br />
c) Answer part (b) assuming that the list contains 99<br />
statements.Mathematical Logichttp://gateoverflow.in/131789/%23propositionlogic-%23rossenSun, 04 Jun 2017 03:45:55 +0000#First order logic
http://gateoverflow.in/131765/%23first-order-logic
<p>Hi,
<br>
<br>
I wanted to know the best way to convert a given<strong> statement to a first order logic</strong>,I was trying to solve the questions related to them but never getting them correct. Could anyone help me in this. I Even had a look in to the videos from <strong>GateBook</strong> it was like I understood the topics But i could not solve ( convert a given<strong> statement to a first order logic)</strong>
<br>
<br>
Thanks in advance</p>Mathematical Logichttp://gateoverflow.in/131765/%23first-order-logicSat, 03 Jun 2017 17:15:55 +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 />
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Use quantifiers and predicates with more than one variable to express these statements.<br />
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a) Every computer science student needs a course in Discrete Mathematics.<br />
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now there is various possible solution for this statement but following the same logic.<br />
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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 />
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$\forall \left ( S(x)\wedge CS(x)\rightarrow DM(x) \right )$<br />
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solution 2) $\forall \left ( P(x) \right )$<br />
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where P(x), x needs a course in DM and domain consist of all computer science student.<br />
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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 />
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A<br />
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A → ( B ∨ C )<br />
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B → ¬A<br />
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conclusion -<br />
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C<br />
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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 />
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UoD : Animals<br />
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The equivalent First Order Logic statement for the above statment is<br />
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$\forall x(Cat(x) )\rightarrow Coffee(x))$<br />
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Lets consider in UoD (animals), let there may be a CAT, TIGER ..etc and consider below statment<br />
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Tiger Drinks Coffee. then the first order logic statment<br />
$\forall x(F \rightarrow T)$<br />
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this statement also satisfying and giving the truth value.<br />
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But our actual statement is 'Every Lion Drinks Coffee' right??<br />
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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