GATE Overflow - Recent questions in Discrete Mathematics
http://gateoverflow.in/questions/mathematics/discrete-mathematics
Powered by Question2AnswerGateoverflow pdf
http://gateoverflow.in/134677/gateoverflow-pdf
<p><img alt="" height="500" src="http://gateoverflow.in/?qa=blob&qa_blobid=12818629108791117556" width="500"></p>Mathematical Logichttp://gateoverflow.in/134677/gateoverflow-pdfSun, 25 Jun 2017 07:51:53 +0000Hasse diagram
http://gateoverflow.in/134666/hasse-diagram
How come D66 is boolean algebra. Explain it through hasse diagram.Set Theory & Algebrahttp://gateoverflow.in/134666/hasse-diagramSun, 25 Jun 2017 04:27:47 +0000Probability
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 +0000Combinatory
http://gateoverflow.in/134611/combinatory
How many ordered quadruples $\left ( x_{1},x_{2},x_{3},x_{4} \right )$ of odd positive integers satisfy<br />
<br />
$$x_{1}+x_{2}+x_{3}+x_{4}=98?$$Combinatoryhttp://gateoverflow.in/134611/combinatorySat, 24 Jun 2017 13:41:31 +0000Recurrence Relation
http://gateoverflow.in/134583/recurrence-relation
<p>The solution of <strong>a<sub>n</sub> = 2a<sub>n-1</sub><sub> </sub>+ 1</strong> where <strong>a<sub>0 </sub>= 1</strong> is ? </p>
<p>Please use the <strong>substitution method</strong> because I seem to have problem understanding it.</p>Combinatoryhttp://gateoverflow.in/134583/recurrence-relationSat, 24 Jun 2017 07:51:08 +0000Combinatorics : Multinomial Coefficients
http://gateoverflow.in/134546/combinatorics-multinomial-coefficients
<p>What's the relationship between combination and polynomial equation? I mean, I am not able to grasp certain points here or let's say connect them into a whole:
<br>
<br>
1. Take a question where it's asked that we have to arrange 10 books : 4 of A, 3 of B, 2 of C, and 1 of D in such a way that each book of similar type remain with its own type so like AAAABBBDCCC, etc. Here we are doing 4!*4!*3!*2!*1!.
<br>
<br>
2. When we take a question of dividing 10 police officers into 3 groups: 10 -> 5,3,2. Here we use 10!/*5!*3!*2!).
<br>
<br>
3. How many solutions of $x1+x2+x3+...+xn=300$ are possible?
<br>
<br>
Doubt: What's the difference between 1 & 2? Isn't two equivalent to saying arrange 10 officers like manner of AAAAABBBCC? If we are grouping 10 distinct elements into 3 groups where each group is of same type, then what's the catch here?
<br>
<br>
Second is what's the similarity between 2 and 3? Isn't three equivalent to saying group 300 distinct element into 3 bags/groups?
<br>
<br>
I am totally confuse here and I think I cannot move ahead with my GATE preparation if I cannot clear my doubt on combinatorics which in turn would mean no way of doing probability's tricky questions.</p>
<p> </p>
<p>EDIT: Here's the images of different questions. How do I differentiate between them?</p>
<p><img alt="" src="http://gateoverflow.in/?qa=blob&qa_blobid=9083059680419989013"><img alt="" src="http://gateoverflow.in/?qa=blob&qa_blobid=14165371670004274780"></p>
<p><img alt="" src="http://gateoverflow.in/?qa=blob&qa_blobid=11854156684812671111"></p>Combinatoryhttp://gateoverflow.in/134546/combinatorics-multinomial-coefficientsSat, 24 Jun 2017 01:58:38 +0000rosen graph theory
http://gateoverflow.in/134449/rosen-graph-theory
find the values (k tuple coloring )<br />
<br />
1)$X_{2}(K_{3}) 2. X_{3}(K_{5})$Graph Theoryhttp://gateoverflow.in/134449/rosen-graph-theoryFri, 23 Jun 2017 07:48:13 +0000Derangements
http://gateoverflow.in/134403/derangements
How many ways we can put 5 letters L1, L2, L3, L4, L5 in 5 envelopes e1, e2, e3, e4 and e5 (at 1 letter per envelope) so that<br />
<br />
i. no letter is correctly placed?<br />
<br />
ii. at least 1 letter is correctly placed?<br />
<br />
iii. exactly 2 letters are correctly placed?<br />
<br />
iv. at most 1 letter is correctly placed?<br />
<br />
v. at least 1 letter is wrongly placed?<br />
<br />
vi. exactly 1 letter is wrongly placed?Combinatoryhttp://gateoverflow.in/134403/derangementsFri, 23 Jun 2017 03:31:20 +0000TESTBOOK TEST
http://gateoverflow.in/134352/testbook-test
<p style="text-align:center"><img alt="" src="http://gateoverflow.in/?qa=blob&qa_blobid=398078124319092299"></p>
<p> </p>Set Theory & Algebrahttp://gateoverflow.in/134352/testbook-testThu, 22 Jun 2017 15:36:04 +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 +0000Self - Doubt
http://gateoverflow.in/133883/self-doubt
What is clique?Graph Theoryhttp://gateoverflow.in/133883/self-doubtMon, 19 Jun 2017 13:44:27 +0000#combinatory
http://gateoverflow.in/133790/%23combinatory
<p><strong>Determine the number of factors of 3<sup>4</sup> * 5<sup>2</sup> * * 11<sup>7</sup> * 13<sup>8</sup>.</strong></p>Combinatoryhttp://gateoverflow.in/133790/%23combinatoryMon, 19 Jun 2017 05:32:07 +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 +0000General Math
http://gateoverflow.in/133745/general-math
Why is $n \leq 2^{h+1} - 1$ equivalent to $h \geq \log_2{\frac{n+1}{2}}$ ? This is applicable to Binary TreesGraph Theoryhttp://gateoverflow.in/133745/general-mathSun, 18 Jun 2017 16:08:26 +0000discrete mathematics , group theory
http://gateoverflow.in/133661/discrete-mathematics-group-theory
Is commutative property sufficient for a group to be abelian?Set Theory & Algebrahttp://gateoverflow.in/133661/discrete-mathematics-group-theorySun, 18 Jun 2017 06:05:28 +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 +0000Set theory
http://gateoverflow.in/133317/set-theory
<p>{ a } ∈ A </p>
<p>but</p>
<p>a ∉ A</p>
<p>why ?</p>
<p>here ' <strong>a is the element of set {a}</strong> ' ,and ' <strong>set {a} is the element of A</strong>" , so " <strong>a also element of A </strong> " . please clear my doubt .</p>Set Theory & Algebrahttp://gateoverflow.in/133317/set-theoryFri, 16 Jun 2017 05:19:09 +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 +0000ISI2017 MMA
http://gateoverflow.in/132738/isi2017-mma
<p>Let S ⊆<em><strong> R. </strong></em></p>
<p>Consider the statement:</p>
<p>"There exists a continuous function f:S -> S such that f(x) != x for all x belongs to S."</p>
<p>This statement is false if S equals</p>
<p>A) [2,3] B) (2,3] c) [-3,-2] union [2,3] D) (-infinity to +infinity)</p>
<p>I think the answer should be D because in -infinity to +infinity, f(x) will definitely be equal to x at some point but we want this to not happen as said in the question. Am I correct?</p>Set Theory & Algebrahttp://gateoverflow.in/132738/isi2017-mmaMon, 12 Jun 2017 07:21:51 +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 +0000Series Summation
http://gateoverflow.in/132690/series-summation
Series summation of $S_n$ in closed form?<br />
<br />
$\begin{align*} &S_n = \frac{1}{1.2.3.4} + \frac{1}{2.3.4.5} + \frac{1}{3.4.5.6} + \dots + \frac{1}{n.(n+1).(n+2).(n+3)} \end{align*}$Set Theory & Algebrahttp://gateoverflow.in/132690/series-summationSun, 11 Jun 2017 16:41:53 +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 #Combinatorics
http://gateoverflow.in/132665/%23discrete-%23combinatorics
The number of ways in which n distinct objects can be put into two identical boxes so that no box remains empty, is<br />
<br />
a) 2^n - 1<br />
<br />
b) 2^n - 2<br />
<br />
c) 2^(n-1) - 1<br />
<br />
d) None of these<br />
<br />
Please explain your answer.Combinatoryhttp://gateoverflow.in/132665/%23discrete-%23combinatoricsSun, 11 Jun 2017 12:33:15 +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 +0000[Discrete Maths] Counting ,Number of solutions to the equation
http://gateoverflow.in/132586/discrete-maths-counting-number-of-solutions-to-the-equation
How many solutions are there to the equation<br />
x1 + x2 + x3 + x4 + x5 = 21,<br />
where xi , i = 1, 2, 3, 4, 5, is a nonnegative integer such that:<br />
<br />
0 ≤ x1 ≤ 3 , 1 ≤ x2 < 4 and 15≤x3 ?Combinatoryhttp://gateoverflow.in/132586/discrete-maths-counting-number-of-solutions-to-the-equationSat, 10 Jun 2017 17:55:46 +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