GATE Overflow - Recent questions in Engineering Mathematics
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Powered by Question2AnswerRelation between Tautology/ Contradiction/ Contingency/ Satisfiability
http://gateoverflow.in/138964/relation-tautology-contradiction-contingency-satisfiability
<p>I am try to develop a venn diagram relation between:-</p>
<p><strong>Tautology/ Contradiction/ Contingency/ Satisfiability </strong></p>
<p>But where I can fit the Contingency in below diagram?<img alt="" src="http://gateoverflow.in/?qa=blob&qa_blobid=1793140421132283631"></p>
<p>I think it should be entirely in the circle of satisfiability and not intersecting with tautology circle.</p>
<p>Correct me if I am wrong?</p>Mathematical Logichttp://gateoverflow.in/138964/relation-tautology-contradiction-contingency-satisfiabilityFri, 21 Jul 2017 02:39:49 +0000Maths
http://gateoverflow.in/138771/maths
<p><a rel="nofollow" href="http://gateoverflow.in/?qa=blob&qa_blobid=3841640957822066036">http://gateoverflow.in/?qa=blob&qa_blobid=3841640957822066036</a></p>
<p> </p>
<p>Can someone show a step wise simplification for this</p>Calculushttp://gateoverflow.in/138771/mathsWed, 19 Jul 2017 18:03:22 +0000planarity is there in syllabus of graph theory or not?
http://gateoverflow.in/138577/planarity-is-there-in-syllabus-of-graph-theory-or-not
Graph Theoryhttp://gateoverflow.in/138577/planarity-is-there-in-syllabus-of-graph-theory-or-notTue, 18 Jul 2017 18:37:22 +0000Gilbert Strang (Books/Video Lectures) Doubt About Which Portions Are Relevant for GATE
http://gateoverflow.in/138463/gilbert-strang-books-video-lectures-doubt-portions-relevant
<p>Hi.</p>
<p>I am trying to prepare for the linear algebra portion for GATE through either Gilbert Strang's video lectures or book.</p>
<p><strong>Can anyone please mention which of Gilbert Strang's video lectures given here </strong></p>
<p><a rel="nofollow" href="https://ocw.mit.edu/courses/mathematics/18-06-linear-algebra-spring-2010/video-lectures/">https://ocw.mit.edu/courses/mathematics/18-06-linear-algebra-spring-2010/video-lectures/ </a></p>
<p><strong>are relevant for gate?</strong></p>
<p>OR</p>
<p><strong>can you mention which chapters/portions from his book <em>Linear Algebra and Its Applications (</em>4th edition) are relevant for GATE?</strong></p>
<p>Thanks a lot!</p>
<p> </p>
<p> </p>Linear Algebrahttp://gateoverflow.in/138463/gilbert-strang-books-video-lectures-doubt-portions-relevantTue, 18 Jul 2017 07:53:42 +0000group theory
http://gateoverflow.in/138460/group-theory
suppose that G IS cycliic group of order 10 with generator "a" belongs to G , order of $a^{8}$ will be ?Set Theory & Algebrahttp://gateoverflow.in/138460/group-theoryTue, 18 Jul 2017 07:27:42 +0000Discreate Random Variable (Rose_8th Edition)
http://gateoverflow.in/138439/discreate-random-variable-rose_8th-edition
Three balls are to be randomly selected without replacement from an urn containing 20 balls numbered 1 through 20. If we bet that at least one of the balls that are drawn has a number as large as or larger than 17, what is the probability that we win the bet?<br />
<br />
My Approach through random variables:<br />
<br />
let X is the random variable defined as:<br />
<br />
X = number of balls having the number on them >= 17 in three drawn.<br />
<br />
In the question, they have asked for at least 1 then we can place the values of X are 1,2,3;<br />
<br />
P(X = 1 ) = (4/20) * (16/19) * (15 / 18) = 0.14035<br />
<br />
P(X = 2 ) = (4/20) * (3/19) * (16 / 18) = 0.02807<br />
<br />
P(X = 3 ) = (4/20) * (3/19) * (2 / 18) = 0.00350<br />
<br />
Prob of wining bet = P(X=1) + P(X=2) + P(X=3) <br />
<br />
= 0.17192<br />
<br />
but the answer is 0.508<br />
<br />
what is wrong with this approach.Combinatoryhttp://gateoverflow.in/138439/discreate-random-variable-rose_8th-editionTue, 18 Jul 2017 05:33:06 +0000sum of n terms
http://gateoverflow.in/138403/sum-of-n-terms
find sum of n terms <br />
<br />
1^2 - 2^2 + 3^2 - 4^2 + 5^2 - 6^2 + ...................<br />
<br />
<br />
<br />
can anyone explain me this how to solve thisMathematical Logichttp://gateoverflow.in/138403/sum-of-n-termsMon, 17 Jul 2017 17:50:25 +0000Generating Function Question
http://gateoverflow.in/138235/generating-function-question
<p>I got (x^20).1/(1+x).1/(1-x)^3 .
<br>
Now, if I write this as -
<br>
[x^20].(1+x)^-1.(1-x)^-3</p>
<p>Now, I don't know how to solve this further when we have both factors having negative n.</p>
<p> </p>
<p>Please don't send me here - <a rel="nofollow" href="http://gateoverflow.in/65803/find-number-integral-solutions-using-generating-function">http://gateoverflow.in/65803/find-number-integral-solutions-using-generating-function</a> </p>
<p>As i Didn't get that solution.</p>
<p> </p>
<p>Someone please simplify it.</p>Combinatoryhttp://gateoverflow.in/138235/generating-function-questionSun, 16 Jul 2017 16:32:02 +0000#limits
http://gateoverflow.in/138136/%23limits
$F(x)= \frac{(4^{x}-1)^{3}}{sin(\frac{x}{p})ln(1+\frac{x^{2}}{3})}$ $( x \neq 0)$<br />
<br />
$F(x)=k. (X=0)$<br />
<br />
Value of p for which $f(x)$ is continuous?Calculushttp://gateoverflow.in/138136/%23limitsSun, 16 Jul 2017 08:15:01 +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 +0000How to find this coefficient in this question?
http://gateoverflow.in/137957/how-to-find-this-coefficient-in-this-question
Find coeff of x^83 in [x^83].(x^5+x^8+x^11+x^14+x^17)Combinatoryhttp://gateoverflow.in/137957/how-to-find-this-coefficient-in-this-questionSat, 15 Jul 2017 08:12:49 +0000Kenneth H Rosen
http://gateoverflow.in/137919/kenneth-h-rosen
Find a compound proposition logically equivalent to p->q using only the logical operator NOR.Mathematical Logichttp://gateoverflow.in/137919/kenneth-h-rosenSat, 15 Jul 2017 01:24:01 +0000Probability # Distribution
http://gateoverflow.in/137764/probability-%23-distribution
A traffic office imposes on an average 5 number of penalities daily on traffic violators.Assume that the number of the penalties on different days is independent and follows a Poisson distribution.The probability that there will be less than 4 penalties in a day is _______________ ?Mathematical Logichttp://gateoverflow.in/137764/probability-%23-distributionFri, 14 Jul 2017 09:22:11 +0000probability
http://gateoverflow.in/137763/probability
a lot consists of 12 good pencils, 6 with minor defects and 2 with major defects. A pencil is chosen at random. The probability that this pencil is not defective is?Probabilityhttp://gateoverflow.in/137763/probabilityFri, 14 Jul 2017 09:19:07 +0000probability
http://gateoverflow.in/137762/probability
a lot consists of good pencils, 6 with minor defects and 2 with major defects. A pencil is chosen at random. The probability that this pencil is not defective is?Probabilityhttp://gateoverflow.in/137762/probabilityFri, 14 Jul 2017 09:18:35 +0000Probability
http://gateoverflow.in/137761/probability
A box contains 4 red balls and 6 black balls .Three balls are selected randomly from the box one after another without replacement .The probability that the selected set contains one red ball and two black ball is <br />
<br />
A)1/20<br />
<br />
B) 1/12<br />
<br />
C) 3/10<br />
<br />
D)1/2Mathematical Logichttp://gateoverflow.in/137761/probabilityFri, 14 Jul 2017 09:13:45 +0000Probability
http://gateoverflow.in/137756/probability
A fair (unbiased) coin was tosssed four times in succession and resulted in the following outcomes:<br />
<br />
i)Head , ii) Head, iii) Head iv)Head. The probability of obtaining a "Tail" when a coin is tossed again is<br />
<br />
A) 0<br />
<br />
B) 1/2<br />
<br />
C) 4/5<br />
<br />
D) 1/5Mathematical Logichttp://gateoverflow.in/137756/probabilityFri, 14 Jul 2017 09:08:30 +0000Probability
http://gateoverflow.in/137755/probability
A fair coin is tossed till a head appears for the first time .The probability that the number of required tosses is odd.<br />
<br />
A) 1/3<br />
<br />
B) 1/2<br />
<br />
C)2/3<br />
<br />
D)3/4Mathematical Logichttp://gateoverflow.in/137755/probabilityFri, 14 Jul 2017 09:01:30 +0000# Probability
http://gateoverflow.in/137733/%23-probability
<p><strong>What is the expected no. of heads that come up when fair coin is flipped five times?</strong></p>Mathematical Logichttp://gateoverflow.in/137733/%23-probabilityFri, 14 Jul 2017 07:03:36 +0000Lattice
http://gateoverflow.in/137535/lattice
Is there any example of lattice which is not bounded ??Set Theory & Algebrahttp://gateoverflow.in/137535/latticeThu, 13 Jul 2017 05:52:16 +0000Question on Number System
http://gateoverflow.in/137519/question-on-number-system
Find the remainder of $\frac{9^{1}+9^{2}+...+9^{n}}{6}$ where $n$ is multiple of 11.<br />
<br />
I am getting $0$ or $3$. But given answer is 3. Can anyone check?Combinatoryhttp://gateoverflow.in/137519/question-on-number-systemThu, 13 Jul 2017 04:32:00 +0000Question on Number System.
http://gateoverflow.in/137518/question-on-number-system
If $N = 1!+2!+3!+...+10!$. What is the last digit of $N^{N}$?Combinatoryhttp://gateoverflow.in/137518/question-on-number-systemThu, 13 Jul 2017 04:07:20 +0000#SETTHEORY
http://gateoverflow.in/137473/%23settheory
Q) Suppose A={a,b,c,d} and Π1 is the following partition of A<br />
<br />
Π1={{a,b,c}{d}}<br />
<br />
And let Π2={{a},{b},{C},{d}} Π3={{a,b,c,d}} and Π4={{a,b},{c,d}},<br />
Draw a Poset diagram of the poset, ⟨{Π1,Π2,Π3,Π4},refines ⟩.<br />
<br />
What does refines means here ?Set Theory & Algebrahttp://gateoverflow.in/137473/%23settheoryWed, 12 Jul 2017 17:31:14 +0000rosen #section 5.5 question 15(d) page no 378
http://gateoverflow.in/137453/rosen-%23section-5-5-question-15-d-page-no-378
Combinatoryhttp://gateoverflow.in/137453/rosen-%23section-5-5-question-15-d-page-no-378Wed, 12 Jul 2017 13:59:53 +0000rosen Exer:5.5 15(c) how many solutions are there for x1+x2+x3+x4+x5=21 such that 0<=x1<=10?(detailed explanation)
http://gateoverflow.in/137443/rosen-exer-many-solutions-there-that-detailed-explanation
Combinatoryhttp://gateoverflow.in/137443/rosen-exer-many-solutions-there-that-detailed-explanationWed, 12 Jul 2017 13:04:02 +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 +0000Discrete Maths Rosen 6th Edition - Is the section 'proofs and strategy' part of the Gate syllabus?
http://gateoverflow.in/137347/discrete-maths-rosen-edition-section-proofs-strategy-syllabus
<p>Hi.</p>
<p>I am new to Gate preparation. It would be very helpful if someone could clarify:</p>
<p><em>Are Section 1.6 and 1.7 (Introduction to Proofs and Proof Methods and Strategy) from Kenneth Rosen (6th Edition) part of the Gate Syllabus?</em></p>
<p>I didn't see them mentioned in the syllabus, hence asking.</p>
<p>Thanks.</p>Mathematical Logichttp://gateoverflow.in/137347/discrete-maths-rosen-edition-section-proofs-strategy-syllabusWed, 12 Jul 2017 01:45:17 +0000What's the coefficient of this expansion??
http://gateoverflow.in/137272/whats-the-coefficient-of-this-expansion
What's the coffecient of x^7 in (2x+4)^10?Mathematical Logichttp://gateoverflow.in/137272/whats-the-coefficient-of-this-expansionTue, 11 Jul 2017 13:39:18 +0000rosen exercise problem
http://gateoverflow.in/137257/rosen-exercise-problem
<p><strong>How many bit strings of length 10 contain at least three 1s and at least three 0s?</strong></p>
<p><strong>My Approach:-></strong></p>
<p><strong>using product rule</strong></p>
<p><strong> There are 3 subtask following</strong></p>
<p><strong><img alt="T_{1}" src="http://latex.codecogs.com/gif.latex?T_%7B1%7D"> (filling 3 ones in 10 places) =<img alt="\binom{10}{3}" src="http://latex.codecogs.com/gif.latex?%5Cbinom%7B10%7D%7B3%7D"></strong></p>
<p><strong><img alt="T_{2}" src="http://latex.codecogs.com/gif.latex?T_%7B2%7D"> (filling 3 zeros in remaing 7 places) =<img alt="\binom{7}{3}" src="http://latex.codecogs.com/gif.latex?%5Cbinom%7B7%7D%7B3%7D"></strong></p>
<p><img alt="T_{3}" src="http://latex.codecogs.com/gif.latex?T_%7B3%7D"> <strong>(filling remaining 4 places) =</strong> <img alt="2^{4}" src="http://latex.codecogs.com/gif.latex?2%5E%7B4%7D"></p>
<p><strong>So,total number of bit string = <img alt="\binom{10}{3}" src="http://latex.codecogs.com/gif.latex?%5Cbinom%7B10%7D%7B3%7D">*<img alt="\binom{7}{3}" src="http://latex.codecogs.com/gif.latex?%5Cbinom%7B7%7D%7B3%7D">*<img alt="2^{4}" src="http://latex.codecogs.com/gif.latex?2%5E%7B4%7D"> which is greater than <img alt="2^{10}" src="http://latex.codecogs.com/gif.latex?2%5E%7B10%7D">(total number of string).</strong></p>
<p><strong>Now , i want to know what is wrong in my apporach. please explain..</strong></p>Combinatoryhttp://gateoverflow.in/137257/rosen-exercise-problemTue, 11 Jul 2017 12:01:02 +0000probability
http://gateoverflow.in/137217/probability
<p><em>India plays two matches each with West I</em><em>ndies</em><em> and Srilanka. In any </em><em>match</em><em> the probabilities of I</em><em>ndia</em><em> getting points 0,1 and 2 are 0.45,0.05 and 0.50 respectively. Assuming that the outcomes are independent, the probability of I</em><em>ndia</em><em> getting </em><em>at least</em><em> 7 points is?</em></p>
<p><em>a) 0.8750 b) 0.0875 c) 0.0625 d) 0.0250</em></p>Probabilityhttp://gateoverflow.in/137217/probabilityTue, 11 Jul 2017 09:10:49 +0000Kenneth Rosen Counting 6.5 Example 6
http://gateoverflow.in/137164/kenneth-rosen-counting-6-5-example-6
<p>What is the value of k after the following pseudocode has been executed?</p>
<pre class="prettyprint">
k := 0
for i1 := 1 to n
for i2 := 1 to i1
·
·
·
for im := 1 to im−1
k := k + 1
</pre>
<p>The solution given is:
<br>
$k = C(n + m − 1,m)$</p>
<p>(A) C(n + m – 1, m)
<br>
(B) C(n – m + 1, m)
<br>
(C) C(n + m – 1, n)
<br>
(D) C(n – m + 1, n) </p>
<p>How do we reach this answer?
<br>
I'm not getting why they used the r-permutation formula here.</p>Combinatoryhttp://gateoverflow.in/137164/kenneth-rosen-counting-6-5-example-6Tue, 11 Jul 2017 03:01:09 +0000How to solve this generating function Question
http://gateoverflow.in/137108/how-to-solve-this-generating-function-question
Given two each of p kinds of objects and one each of additional q kind of objects, in how many ways r objects can be selected?<br />
<br />
Please give a detailed solution.Mathematical Logichttp://gateoverflow.in/137108/how-to-solve-this-generating-function-questionMon, 10 Jul 2017 12:38:07 +0000Doubt
http://gateoverflow.in/136941/doubt
What is mode of 1,2,3,3,4,4 ?Probabilityhttp://gateoverflow.in/136941/doubtSun, 09 Jul 2017 15:06:37 +0000Generating Functions Topic Query
http://gateoverflow.in/136893/generating-functions-topic-query
<p>What are the prerequisite to understand Generating Function?</p>
<p>I tried Rosen book, but I didn't get anything from it except the fact that there's some power series involvement in it. </p>
<p>Now, I don't know calculas at all. So, I don't know anything about Power series. </p>
<p>Then I tried watching this video of IIT MADRAS - <a rel="nofollow" href="https://www.youtube.com/watch?v=4d2XEn1j_q4&t=2765s">Lecture 30 - Generating Functions</a> but it has some serious audio/video lag and I'm not able to make much form this video!</p>
<p> </p>
<p>SO, anyone tell me what are things required to understand Generating Function.</p>
<p>P.S - I studied Binomial Theorem Chapter from Class 11th Cbse as binomial expansions are used in generating function.</p>
<p>Please tell me, I'm unable to understand this topic at all.</p>
<p>Thanks</p>Mathematical Logichttp://gateoverflow.in/136893/generating-functions-topic-querySun, 09 Jul 2017 10:53:49 +0000gatebook
http://gateoverflow.in/136871/gatebook
How many bit strings of length 6 have more no of zeros than ones??<br />
<br />
<br />
<br />
We can solve this drawing tree but it takes so much time Is there any other way??Combinatoryhttp://gateoverflow.in/136871/gatebookSun, 09 Jul 2017 08:47:05 +0000GATEbook
http://gateoverflow.in/136859/gatebook
<p><img alt="" src="http://gateoverflow.in/?qa=blob&qa_blobid=7509052260239437586"></p>Combinatoryhttp://gateoverflow.in/136859/gatebookSun, 09 Jul 2017 07:20:17 +0000Gatebook
http://gateoverflow.in/136829/gatebook
<p><img alt="" src="http://gateoverflow.in/?qa=blob&qa_blobid=11790649760514761116"></p>
<p> </p>
<p>I am not able to understand the last component in square brackets we have to minus from all combinations the combinations with that dotted line but intersection part i didn't get</p>Combinatoryhttp://gateoverflow.in/136829/gatebookSun, 09 Jul 2017 02:46:56 +0000Please suggest material for graph theory .
http://gateoverflow.in/136778/please-suggest-material-for-graph-theory
Please suggest material for graph theory .Graph Theoryhttp://gateoverflow.in/136778/please-suggest-material-for-graph-theorySat, 08 Jul 2017 17:26:47 +0000graph theory
http://gateoverflow.in/136745/graph-theory
can we say a null graph is eulerian circuit and hamiltonian circuit?Mathematical Logichttp://gateoverflow.in/136745/graph-theorySat, 08 Jul 2017 14:02:39 +0000Rosen
http://gateoverflow.in/136736/rosen
Find the edge chromatic numbers of<br />
a) Cn, where n ≥ 3. (Cycle with n vertices)<br />
<br />
b) Wn, where n ≥ 3 (Wheel with n vertices)<br />
<br />
c)Complete graph with n vertices.Engineering Mathematicshttp://gateoverflow.in/136736/rosenSat, 08 Jul 2017 13:26:57 +0000Rosen Counting Permutations
http://gateoverflow.in/136682/rosen-counting-permutations
I was doing two Questions of rosen counting chapter<br />
<br />
Q1. A group contains n mens and n women. How many ways are there to "arrange" these people in a row if the men and women alternate ?<br />
<br />
Answer is 2(n!)^2, I agree with logic and answer.<br />
<br />
<br />
<br />
Q2. How many ways are there for eight men and five women to stand in a line so that no two women stand next to each other?<br />
<br />
Answer is P(8,8)*P(9,5), I also agree with answer and logic.<br />
<br />
<br />
<br />
My dobut is, The frame of questions are similar but then why can't we solve Q1 with the approach used in Q2 i.e. first permuting n men and then choosing n women places from (n+1) places created my positioning the men and permuting them again i.e P(n,n)*P(n+1,n) ??Combinatoryhttp://gateoverflow.in/136682/rosen-counting-permutationsSat, 08 Jul 2017 07:32:52 +0000algorithm
http://gateoverflow.in/136521/algorithm
<p>.<img alt="" src="http://gateoverflow.in/?qa=blob&qa_blobid=14753053917675909609">a A nswer is nlogn by master method , but iam not able to solve this equation by this method can any one solve this and please tell me where iam wrong thanks</p>Mathematical Logichttp://gateoverflow.in/136521/algorithmFri, 07 Jul 2017 12:02:31 +0000Relation and Partial order
http://gateoverflow.in/136517/relation-and-partial-order
<p> </p>
<p>Is (<em>S, R</em>) a <strong>poset </strong>if <em>S </em>is the set of all people in the world and (<em>a, b</em>) <em>∈ </em><em>R</em>, where <em>a </em>and <em>b </em>are people,
<br>
if <strong><em>a </em>is not taller than <em>b</em></strong>?
<br>
</p>Set Theory & Algebrahttp://gateoverflow.in/136517/relation-and-partial-orderFri, 07 Jul 2017 11:35:52 +0000algorithm
http://gateoverflow.in/136494/algorithm
. T (n) = 3T (n/2) + n <br />
<br />
<br />
<br />
i can apply masters theorem and solve it , can i solve it by back substitution too , but i dont know base condition ??? how can i solve itMathematical Logichttp://gateoverflow.in/136494/algorithmFri, 07 Jul 2017 09:10:58 +0000maths
http://gateoverflow.in/136485/maths
<p>log<sup>2</sup>n is equal to logn*logn.</p>
<p> </p>
<p> </p>
<p>_____ is equal to log(log n) </p>
<p> </p>
<p>what should be there in blank </p>Mathematical Logichttp://gateoverflow.in/136485/mathsFri, 07 Jul 2017 08:49:32 +0000graph
http://gateoverflow.in/136184/graph
a tree with n vertices can have at most 1 perfect matching how?<br />
<br />
<br />
<br />
<br />
<br />
perfect matching means no vertices will be left with 0 dergree right so how a tree can have a perfect matching <br />
<br />
explain with the help of trees plzMathematical Logichttp://gateoverflow.in/136184/graphWed, 05 Jul 2017 14:21:29 +0000Problem related to Equivalence relation
http://gateoverflow.in/136171/problem-related-to-equivalence-relation
<h3><strong>R </strong>is a relation on the set of all <strong>functions </strong>from <strong>Z </strong>to <strong>Z</strong>.</h3>
<h3><strong>R = { (f, g) | for some C ∈ Z , for all x ∈ Z , f(x) - g(x) = C } </strong></h3>
<p>is it <strong>Equivalence relation </strong>or not ?</p>Set Theory & Algebrahttp://gateoverflow.in/136171/problem-related-to-equivalence-relationWed, 05 Jul 2017 13:13:30 +0000Linear Algebra by Gilbert strang, 4th edition, 5.1.13
http://gateoverflow.in/136154/linear-algebra-by-gilbert-strang-4th-edition-5-1-13
If B has eigenvalues 1, 2, 3, C has eigenvalues 4, 5, 6, and D has eigenvalues 7, 8,<br />
9, what are the eigenvalues of the 6 by 6 matrix A =[ B C , 0 D] ?Linear Algebrahttp://gateoverflow.in/136154/linear-algebra-by-gilbert-strang-4th-edition-5-1-13Wed, 05 Jul 2017 11:14:33 +0000Kenneth Rosen logic and proof example 21
http://gateoverflow.in/136097/kenneth-rosen-logic-and-proof-example-21
Negation of ∃ x(x^2=2) should be ∀x (x^2!=2).But in the book it's given as ∀x(x^2=2). I think it is misprint. Please correct me if I m wrong.<br />
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Thank you in advance.Mathematical Logichttp://gateoverflow.in/136097/kenneth-rosen-logic-and-proof-example-21Wed, 05 Jul 2017 05:15:41 +0000