GATE Overflow - Recent questions in Mathematical Logic
http://gateoverflow.in/questions/mathematics/discrete-mathematics/mathematical-logic
Powered by Question2AnswerPropositional function doubt
http://gateoverflow.in/145315/propositional-function-doubt
The Number of n-variable propositional function ?<br />
<br />
a. 2^2^n.<br />
<br />
b.2^n^2<br />
<br />
c.2^n<br />
<br />
d. n^2<br />
<br />
Can any one please explain the what should be the answer and how to get it?Mathematical Logichttp://gateoverflow.in/145315/propositional-function-doubtFri, 18 Aug 2017 18:07:26 +0000solution of rosen
http://gateoverflow.in/145129/solution-of-rosen
can anyone has the soft copy of kenneth h rosen solutions?Mathematical Logichttp://gateoverflow.in/145129/solution-of-rosenFri, 18 Aug 2017 06:40:06 +0000number of comparison
http://gateoverflow.in/145116/number-of-comparison
how many comparison are needed to locate the maximum and minimum in a sequence with 128 elements?Mathematical Logichttp://gateoverflow.in/145116/number-of-comparisonFri, 18 Aug 2017 05:56:24 +0000Mott Kandel Baker Ex. 1.7 Q. 23
http://gateoverflow.in/145084/mott-kandel-baker-ex-1-7-q-23
The circumference of two concentric disks is divided into 200 sections each. For the outer disk, 100 of the sections are painted red and 100 are painted white. For the inner disk, the sections are painted red or white in an arbitrary manner. Show that it is possible to align the 2 disks so that 100 or more of the sections of inner disk have their colors matched with the corresponding sections on the outer disk.Mathematical Logichttp://gateoverflow.in/145084/mott-kandel-baker-ex-1-7-q-23Fri, 18 Aug 2017 03:56:03 +0000Relation doubt
http://gateoverflow.in/144870/relation-doubt
What is the total number of asymmetric and transitive relation from set a to itself which has n element ?Mathematical Logichttp://gateoverflow.in/144870/relation-doubtThu, 17 Aug 2017 08:53:28 +0000how to draw this graph plz explain in detail
http://gateoverflow.in/144686/how-to-draw-this-graph-plz-explain-in-detail
y = | x^2- 2 | how to draw graph of such equationMathematical Logichttp://gateoverflow.in/144686/how-to-draw-this-graph-plz-explain-in-detailWed, 16 Aug 2017 16:09:01 +0000check this ? is graph correct ? how to find other points
http://gateoverflow.in/144509/check-this-is-graph-correct-how-to-find-other-points
<p><img alt="" src="http://gateoverflow.in/?qa=blob&qa_blobid=1350301987973177666"></p>Mathematical Logichttp://gateoverflow.in/144509/check-this-is-graph-correct-how-to-find-other-pointsWed, 16 Aug 2017 07:24:35 +0000Kenneth Rosen 7th edition Propositional Logic Ex. 1.2 question 38
http://gateoverflow.in/144353/kenneth-rosen-7th-edition-propositional-logic-ex-question
Solve this famous logic puzzle, attributed to Albert Einstein, and known as the zebra puzzle. Five men with different nationalities and with different jobs live in consecutive houses on a street. These houses are painted different colours. The men have different pets and have different favourite drinks. Determine who owns a zebra and whose favourite drink is mineral water (which is one of the favourite drinks) given these clues: The Englishman lives in the red house. The Spaniard owns a dog. The Japanese man is a painter. The Italian drinks tea. The Norwegian lives in the first house on the left. The green house is immediately right of the white one. The photographer breeds snails. The diplomat lives in the yellow house. Milk is drunk in the middle house. The owner of the green house drinks coffee. The Norwegian’s house is next to the blue one. The violinist drinks orange juice. The fox is in a house next to that of the physician. The horse is in a house next to that of the diplomat. [Hint: Make a table where the rows represent the men and columns represent the colour of their houses, their jobs, their pets, and their favourite drinks and use logical reasoning to determine the correct entries in the table.]Mathematical Logichttp://gateoverflow.in/144353/kenneth-rosen-7th-edition-propositional-logic-ex-questionTue, 15 Aug 2017 12:40:08 +0000Mathematical logic
http://gateoverflow.in/143835/mathematical-logic
Let P, Q and R be three atomic propositional assertion. Let X denote (PvQ)$\rightarrow$R and Y denote (P$\rightarrow$R)v(Q$\rightarrow$R). Which of the following is a tautology? <br />
<br />
(A) X$equiv$Y<br />
<br />
(B) X$\rightarrow$Y<br />
<br />
(C) Y$\rightarrow$X<br />
<br />
(D) $\dashv$Y$\rightarrow$ $\dashv$X<br />
<br />
ExplainMathematical Logichttp://gateoverflow.in/143835/mathematical-logicSun, 13 Aug 2017 14:32:09 +0000Rosen_Discrete_Mathematics_and_Its_Applications_7th_Edition/Pg.56/Section 1.4 :predicates and quantifiers/Q.43 and Q.44
http://gateoverflow.in/143763/rosen_discrete_mathematics_and_its_applications_7th_edition
43. Determine whether ∀x(P(x)→Q(x)) and ∀xP (x)→∀xQ(x) are logically equivalent. Justify your answer.<br />
<br />
44. Determine whether ∀x(P(x)↔Q(x)) and ∀ x P (x) ↔ ∀ xQ(x) are logically equivalent. Justify your answer.<br />
<br />
<br />
<br />
First I would like to know , how to proceed with such type of questions and what would be the solution..Mathematical Logichttp://gateoverflow.in/143763/rosen_discrete_mathematics_and_its_applications_7th_editionSun, 13 Aug 2017 08:28:08 +0000Mathematical logic
http://gateoverflow.in/143744/mathematical-logic
Consider the logical inference :<br />
<br />
I : if it rains then the cricket match will not be played. <br />
<br />
It did not rain<br />
<br />
Inference :the cricket match was played. <br />
<br />
Is the inference I correct? <br />
<br />
ExplainMathematical Logichttp://gateoverflow.in/143744/mathematical-logicSun, 13 Aug 2017 07:05:17 +0000Proposition
http://gateoverflow.in/143687/proposition
X posed many puzzles about an island that has two kinds of inhabitants knights who always tells the truth, and their opposite knaves, who always lie. You encounter two people A and B. What are A and B if A says 'B is a knight' and B says 'two of us are of opposite types'?Mathematical Logichttp://gateoverflow.in/143687/propositionSun, 13 Aug 2017 02:40:53 +0000quantifiers
http://gateoverflow.in/143495/quantifiers
In rosen it is given that ∃xp(x) is false when the domain is empty but what about value of ∀xp(x) when the domain is empty ?Mathematical Logichttp://gateoverflow.in/143495/quantifiersSat, 12 Aug 2017 06:56:27 +0000Discrete mathematics ex 1.5
http://gateoverflow.in/143198/discrete-mathematics-ex-1-5
How to solve this kind of questions...<br />
<br />
What rules of inference are used in this argument?<br />
<br />
No man is an island<br />
<br />
Manhattan is an island<br />
<br />
Therefore,<br />
<br />
Manhattan is not a man.Mathematical Logichttp://gateoverflow.in/143198/discrete-mathematics-ex-1-5Fri, 11 Aug 2017 06:18:02 +0000equivalence relation: rosen exercise question
http://gateoverflow.in/143177/equivalence-relation-rosen-exercise-question
1- these relations on the set of all functions from Z to Z. Determine the properties they lack for equivalence relation?<br />
<br />
a) {(f, g) | f (0) = g(0) or f (1) = g(1)}<br />
<br />
b) {(f, g) | f (0) = g(1) and f (1) = g(0)}Mathematical Logichttp://gateoverflow.in/143177/equivalence-relation-rosen-exercise-questionFri, 11 Aug 2017 05:27:11 +0000Discrete mathematics
http://gateoverflow.in/143170/discrete-mathematics
Proofs questions are asked in mathematical logic gate?Mathematical Logichttp://gateoverflow.in/143170/discrete-mathematicsFri, 11 Aug 2017 04:23:14 +0000Discrete mathematics exercise 1.5 6
http://gateoverflow.in/143036/discrete-mathematics-exercise-1-5-6
Use rules of inference to show that the hypothesis<br />
<br />
" If it doesn't rain or it is not foggy, then the sailing race will be held and the lifesaving demonstration will go on ".<br />
<br />
"If the sailing race is held, then the trophy will be awarded"<br />
<br />
"The trophy was not awarded".<br />
<br />
Imply the conclusion "It rained".Mathematical Logichttp://gateoverflow.in/143036/discrete-mathematics-exercise-1-5-6Thu, 10 Aug 2017 14:40:00 +0000J.P TREMBLAY EXCERCISE 1-4.1 4 TH QUESTION
http://gateoverflow.in/142810/j-p-tremblay-excercise-1-4-1-4-th-question
<p><img alt="" src="http://gateoverflow.in/?qa=blob&qa_blobid=12482066827450809867"></p>Mathematical Logichttp://gateoverflow.in/142810/j-p-tremblay-excercise-1-4-1-4-th-questionWed, 09 Aug 2017 16:47:33 +0000Discrete mathematics example 13 Kenneth rosen
http://gateoverflow.in/142589/discrete-mathematics-example-13-kenneth-rosen
<p>How can sentence be translated into a logical expression ?</p>
<p><em><strong>"You can't ride the roller coaster if you are under 4 feet tall unless you are older than 16 years old".</strong></em></p>
<p>Can answer be (!s->r)->!q</p>
<p>Where</p>
<p>q= You can ride the roller coaster</p>
<p>r=You are under 4 feet tall</p>
<p>s= You are older than 16 years old</p>
<p> </p>Mathematical Logichttp://gateoverflow.in/142589/discrete-mathematics-example-13-kenneth-rosenWed, 09 Aug 2017 02:39:08 +0000probability
http://gateoverflow.in/142502/probability
<p><img alt="" src="http://gateoverflow.in/?qa=blob&qa_blobid=5164991502263664022"></p>Mathematical Logichttp://gateoverflow.in/142502/probabilityTue, 08 Aug 2017 14:49:42 +0000number of paths in a graph
http://gateoverflow.in/142407/number-of-paths-in-a-graph
Find the number of paths of length n between two different vertices in K4 if n is<br />
a) 2. b) 3. c) 4. d) 5.Mathematical Logichttp://gateoverflow.in/142407/number-of-paths-in-a-graphTue, 08 Aug 2017 05:38:07 +0000Limits
http://gateoverflow.in/142404/limits
can you please solve <br />
<br />
lt x->1 x^3-x^2logx+logx-1/x^2-1<br />
<br />
using L-Hospitals ruleMathematical Logichttp://gateoverflow.in/142404/limitsTue, 08 Aug 2017 05:16:59 +0000J P TREMBLAY R MANOHAR EXCERCISE1-2.11
http://gateoverflow.in/142352/j-p-tremblay-r-manohar-excercise1-2-11
P->(Q->P) IS EQUIVALENT TO ~P->(P->Q) WITHOUT USING TRUTH TABLEMathematical Logichttp://gateoverflow.in/142352/j-p-tremblay-r-manohar-excercise1-2-11Mon, 07 Aug 2017 16:39:55 +0000doubt
http://gateoverflow.in/142307/doubt
Given 3 characters a, b, c. Find the number of strings of length n that can be formed from these 3 characters. Given that : we can use ‘a’ as many times as we want, ‘b’ maximum once, and ‘c’ maximum twice.Mathematical Logichttp://gateoverflow.in/142307/doubtMon, 07 Aug 2017 13:29:44 +0000hey can i do this is it allowed , and if not then someone plz solve it
http://gateoverflow.in/142106/hey-can-do-this-is-it-allowed-and-if-not-then-someone-plz-solve
<p><img alt="" src="http://gateoverflow.in/?qa=blob&qa_blobid=2555709503946725421"></p>Mathematical Logichttp://gateoverflow.in/142106/hey-can-do-this-is-it-allowed-and-if-not-then-someone-plz-solveSun, 06 Aug 2017 14:03:21 +0000Discrete 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 +0000limit
http://gateoverflow.in/141545/limit
<p><img alt="" src="http://gateoverflow.in/?qa=blob&qa_blobid=10373891896846159907"></p>Mathematical Logichttp://gateoverflow.in/141545/limitFri, 04 Aug 2017 04:25:45 +0000eigen value
http://gateoverflow.in/141476/eigen-value
<p><img alt="" src="http://gateoverflow.in/?qa=blob&qa_blobid=5840459314297349758"></p>Mathematical Logichttp://gateoverflow.in/141476/eigen-valueThu, 03 Aug 2017 14:00:09 +0000Linear algebra
http://gateoverflow.in/141197/linear-algebra
How we find eigen values from characteristics equation ?<br />
<br />
Steps please.Mathematical Logichttp://gateoverflow.in/141197/linear-algebraWed, 02 Aug 2017 08:28:43 +0000Differentiation
http://gateoverflow.in/141155/differentiation
Mathematical Logichttp://gateoverflow.in/141155/differentiationWed, 02 Aug 2017 04:50:09 +0000linear algebra
http://gateoverflow.in/141153/linear-algebra
<p><img alt="" src="http://gateoverflow.in/?qa=blob&qa_blobid=10136455710427029664"></p>Mathematical Logichttp://gateoverflow.in/141153/linear-algebraWed, 02 Aug 2017 04:17:49 +0000linear algebra
http://gateoverflow.in/141151/linear-algebra
<p><img alt="" src="http://gateoverflow.in/?qa=blob&qa_blobid=4754910971192488066"></p>Mathematical Logichttp://gateoverflow.in/141151/linear-algebraWed, 02 Aug 2017 04:16:25 +0000Probability
http://gateoverflow.in/141111/probability
Consider the experiment of throwing a die, if a multiple of 3 comes up, throw the<br />
die again and if any other number comes, toss a coin. Find the conditional probability<br />
of the event ‘the coin shows a tail’, given that ‘at least one die shows a 3’Mathematical Logichttp://gateoverflow.in/141111/probabilityTue, 01 Aug 2017 20:07:36 +0000Probability: Poisson distribution calculation vs normal probability calculation
http://gateoverflow.in/141096/probability-distribution-calculation-probability-calculation
<p><img alt="" src="http://gateoverflow.in/?qa=blob&qa_blobid=6871126998631182856"></p>
<p>In this question if we do simply probability calculation then it is 8/20 40%</p>
<p>but when I am appling poisson distribution then it is 40.4%.</p>
<p>why we are getting two different answers??</p>Mathematical Logichttp://gateoverflow.in/141096/probability-distribution-calculation-probability-calculationTue, 01 Aug 2017 18:18:46 +0000Homogeneous equations.
http://gateoverflow.in/141009/homogeneous-equations
How we decide about the random value used in liner homogeneous equation ? Any trick or way to get that random value.Mathematical Logichttp://gateoverflow.in/141009/homogeneous-equationsTue, 01 Aug 2017 09:32:12 +0000linear algebra
http://gateoverflow.in/140628/linear-algebra
Rank of matrix :<br />
<br />
1) Rank is equal to the number of linearly independent rows or columns in the matrix <br />
<br />
2)Rank is equal to the number of non zero rows in ECHLON FORM of matrix<br />
<br />
ARE BOTH the things same pls explain ?Mathematical Logichttp://gateoverflow.in/140628/linear-algebraSun, 30 Jul 2017 06:19:17 +0000linear algebra
http://gateoverflow.in/140610/linear-algebra
How many different entries can a 4 * 4 skew-symmetric matrix have? An n* n skew-symmetric matrix? What if it is symmetric matrix ?Mathematical Logichttp://gateoverflow.in/140610/linear-algebraSun, 30 Jul 2017 04:50:49 +0000Rosen
http://gateoverflow.in/140603/rosen
$0,1,0,0,1,0,0,1,.......$<br />
<br />
The answer is $f(x) = \frac{x}{1-x^3}$ ?Mathematical Logichttp://gateoverflow.in/140603/rosenSun, 30 Jul 2017 03:24:46 +0000Rosen
http://gateoverflow.in/140597/rosen
Everyone has exactly one best friend. Domain consist of all people. Write the logical expression involving predicate and quantifier.Mathematical Logichttp://gateoverflow.in/140597/rosenSun, 30 Jul 2017 00:36:31 +0000Linear algebra Determinant
http://gateoverflow.in/140336/linear-algebra-determinant
<p>True/False</p>
<p>A matrix is singular <strong>iff </strong>any row/column is constant multiple of any other row/column?</p>
<p> </p>Mathematical Logichttp://gateoverflow.in/140336/linear-algebra-determinantFri, 28 Jul 2017 14:41:38 +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 +0000One to one function
http://gateoverflow.in/140242/one-to-one-function
<p>Following is the way of checking the one to one function</p>
<p><img alt="{\displaystyle \forall a,b\in X,\;\;a\neq b\Rightarrow f(a)\neq f(b)}" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d52ee1d110aeb9914f2a139916a7d498cbb3e4e3"></p>
<p>or</p>
<p><img alt="{\displaystyle \forall a,b\in X,\;\;f(a)=f(b)\Rightarrow a=b}" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/fa7a1e37af3c3a313a7a23a2b49e7c68fc7135aa"></p>
<p>Can i use bi implication in between these?If not,then why?</p>Mathematical Logichttp://gateoverflow.in/140242/one-to-one-functionThu, 27 Jul 2017 17:04:03 +0000Kenneth Rosen ,DM and its Application Exercise 1.5 Qn 35
http://gateoverflow.in/139839/kenneth-rosen-dm-and-its-application-exercise-1-5-qn-35
Find a common domain for the variables x, y, z,<br />
and w for which the statement $∀x∀y∀z∃w((w \neq x) ∧ (w \neq y) ∧ (w \neq z))$ is true and another common domain<br />
for these variables for which it is false.Mathematical Logichttp://gateoverflow.in/139839/kenneth-rosen-dm-and-its-application-exercise-1-5-qn-35Tue, 25 Jul 2017 15:40:04 +0000#Rosen
http://gateoverflow.in/139694/%23rosen
<p>Let P(x), Q(x), and R(x) be the statements “x is a
<br>
professor,” “x is ignorant,” and “x is vain,” respectively.
<br>
Express each of these statements using quantifiers; logical
<br>
connectives; and P(x), Q(x), and R(x), where the
<br>
domain consists of all people.</p>
<ul>
<li><strong>a) No professors are ignorant.</strong></li>
<li><strong>b) All ignorant people are vain.</strong></li>
<li><strong>c) No professors are vain.</strong></li>
</ul>
<p>Can someone explain each of the given Predicates?</p>Mathematical Logichttp://gateoverflow.in/139694/%23rosenMon, 24 Jul 2017 22:26:35 +0000rosen
http://gateoverflow.in/139114/rosen
<p><img alt="" src="http://gateoverflow.in/?qa=blob&qa_blobid=4071415644195802363"></p>Mathematical Logichttp://gateoverflow.in/139114/rosenSat, 22 Jul 2017 03:40:33 +0000Rosen page no. 45 question no. 29 (c) section 1.3
http://gateoverflow.in/139107/rosen-page-no-45-question-no-29-c-section-1-3
Express in logical operators, predicate and quantifier.<br />
<br />
The disjunction of two contingencies can be a tautology.Mathematical Logichttp://gateoverflow.in/139107/rosen-page-no-45-question-no-29-c-section-1-3Sat, 22 Jul 2017 00:42:14 +0000MIT Assignment: Preposition Logic
http://gateoverflow.in/139071/mit-assignment-preposition-logic
<p><img alt="" src="http://gateoverflow.in/?qa=blob&qa_blobid=474484481102173071"></p>
<p>a) x = 1.</p>
<p>b) m is a divisor of n(notation: m|n).</p>
<p>c) n is a prime number.</p>
<p>d) n is a power of a prime.</p>
<p> </p>Mathematical Logichttp://gateoverflow.in/139071/mit-assignment-preposition-logicFri, 21 Jul 2017 17:24:03 +0000Preposition logic "At most" statement
http://gateoverflow.in/139027/preposition-logic-at-most-statement
How to write:-<br />
<br />
"There are at most two apples"<br />
<br />
I think it should be:-<br />
<br />
∀x { A(x) -> ∀y {A(y) -> (x=y) V [ ∀z [A(z) -> ((z=y) V (z=x))]]}}<br />
<br />
is it correct or not?Mathematical Logichttp://gateoverflow.in/139027/preposition-logic-at-most-statementFri, 21 Jul 2017 11:19:00 +0000suggestion
http://gateoverflow.in/139020/suggestion
in gate few questions came frm generating functions how to solve them ????Mathematical Logichttp://gateoverflow.in/139020/suggestionFri, 21 Jul 2017 10:28:24 +0000