GATE Overflow - Recent questions tagged discrete-mathematics
https://gateoverflow.in/tag/discrete-mathematics
Powered by Question2AnswerGraph theory
https://gateoverflow.in/162137/graph-theory
What type of graph is STAR?<br />
<br />
A. Bipartite<br />
<br />
B. Tripartite<br />
<br />
C. Mutipartite<br />
<br />
PS : I know a star graph is bipartite but can't we say that a bipartite graph is also tripartite . I. E. It can be partitioned into 3 independent sets.<br />
<br />
Similarly , it is mutipartite as well.Othershttps://gateoverflow.in/162137/graph-theoryMon, 23 Oct 2017 08:38:24 +0000Kenneth Rosen chapter 6.4 question no 35
https://gateoverflow.in/161726/kenneth-rosen-chapter-6-4-question-no-35
How many bit strings contain exactly eight 0s and 10 1s if every 0 must be immediately followed by a 1?Combinatoryhttps://gateoverflow.in/161726/kenneth-rosen-chapter-6-4-question-no-35Sat, 21 Oct 2017 05:17:26 +0000Solution of non - homogeneous Recurrence relation
https://gateoverflow.in/161589/solution-of-non-homogeneous-recurrence-relation
<p>How following recurrence relation could be solved (means via Homogenous solution and particular solution method) --></p>
<p>H(n) = H(2/3(n-1)) + 1
<br>
H(1) = 0</p>
<p>PS: One way to solve it is mentioned here <a rel="nofollow" href="https://gateoverflow.in/842/gate2002-2-12">https://gateoverflow.in/842/gate2002-2-12</a>. But how it could be solved via Homogenous solution and particular solution method.</p>Combinatoryhttps://gateoverflow.in/161589/solution-of-non-homogeneous-recurrence-relationFri, 20 Oct 2017 11:23:25 +0000First Order Logic
https://gateoverflow.in/161096/first-order-logic
A = ∃x (P(x) ^ Q(x)).<br />
<br />
B = ∃x P(x) ^ ∃x Q(x).<br />
<br />
Which is correct?<br />
<br />
a) A => B<br />
<br />
b) B => A<br />
<br />
c) A <=> B<br />
<br />
d) None of These<br />
<br />
Please Explain.Mathematical Logichttps://gateoverflow.in/161096/first-order-logicWed, 18 Oct 2017 13:58:39 +0000First Order Logic
https://gateoverflow.in/161094/first-order-logic
A = ∃x(P(x)^Q(x))<br />
<br />
B = ∃x P(x) ^ ∃x Q(x), which is correct?<br />
<br />
a) A <=> B<br />
<br />
b) A => B<br />
<br />
c) B => A<br />
<br />
d) None of These<br />
<br />
Please Explain.Mathematical Logichttps://gateoverflow.in/161094/first-order-logicWed, 18 Oct 2017 13:56:07 +0000Made easy
https://gateoverflow.in/160388/made-easy
<p><img alt="" src="https://gateoverflow.in/?qa=blob&qa_blobid=3453992012750236024"></p>
<p> </p>
<p> </p>
<p>Please tell me how the odd function is getting a positive value over -1/2 to 1/2?</p>Mathematical Logichttps://gateoverflow.in/160388/made-easySun, 15 Oct 2017 17:59:11 +0000Previous year
https://gateoverflow.in/160006/previous-year
Consider the function f(x)=sin(x) in the interval x=[π/4,7π/4]. The number and location(s) of the local minima of this function are<br />
<br />
(A) One, at π/2<br />
(B) One, at 3π/2<br />
(C) Two, at π/2 and 3π/2<br />
(D) Two, at π/4 and 3π/2<br />
<br />
Please explain how pie/4 is local minima ? I mean when do we consider extreme points for local minima? in books they consider only for f'(x) =0 that is points where slope is 0 for f(x) not the end points.End points is used for absolute minima/maxima ( as much as i have read in books that is).Mathematical Logichttps://gateoverflow.in/160006/previous-yearSat, 14 Oct 2017 15:02:41 +0000K. Rosen: Countings
https://gateoverflow.in/159361/k-rosen-countings
<p><strong>Question</strong> How many different strings of length 2 can be made from the letters in '<strong>ORONO</strong>'?</p>
<p>I am getting 7 strings as follows: OO, ON, OR, NO, RO, RN, NR
<br>
but given<strong> answer is 6</strong>.</p>
<p> </p>Combinatoryhttps://gateoverflow.in/159361/k-rosen-countingsThu, 12 Oct 2017 05:16:46 +0000Kneath Rosen: DM: Counting
https://gateoverflow.in/159332/kneath-rosen-dm-counting
<p><img alt="" src="http://gateoverflow.in/?qa=blob&qa_blobid=7471213247320786666"></p>
<p>Following is the given solution in the solution manual:</p>
<p><img alt="" src="http://gateoverflow.in/?qa=blob&qa_blobid=9160356175295703191"></p>
<p>I understood how we got x1 + x2 + x3 + x4 + x5 = 5, I understood too how we got x1+x2+x3+x4+x5 = 1, when x1>=4.</p>
<p>but I am unable to understand the highlighted part. how did we get x1 + x2 + x3 + x4 + x5 = 2. please explain.</p>
<p>PS: i solved this question using generating functions and i am getting the same answer as 106.</p>Algorithmshttps://gateoverflow.in/159332/kneath-rosen-dm-countingWed, 11 Oct 2017 23:46:37 +0000#self_doubt #
https://gateoverflow.in/158921/%23self_doubt-%23
1.how many outcome are appear if the dice thrown 10 times ?<br />
and<br />
2.how many way to arrange (1,2,3....13) into 8x8 matrix <br />
<br />
#doubt _both are looking same question but in 1st we apply diffrent method and in 2nd we apply diff so <br />
can we avoid these type of doubt...Combinatoryhttps://gateoverflow.in/158921/%23self_doubt-%23Tue, 10 Oct 2017 06:38:37 +0000generating function
https://gateoverflow.in/158597/generating-function
<p><strong>generating function shifted Fibonacci sequence</strong> </p>
<p>(what we actually do while finding generating function)</p>Combinatoryhttps://gateoverflow.in/158597/generating-functionMon, 09 Oct 2017 09:47:29 +0000#discrete mathematics
https://gateoverflow.in/158370/%23discrete-mathematics
Are Conjunctive Normal Form and Disjunctive Normal Form included in the GATE syllabus?Mathematical Logichttps://gateoverflow.in/158370/%23discrete-mathematicsSun, 08 Oct 2017 15:55:52 +0000# doubt
https://gateoverflow.in/158148/%23-doubt
<p><img alt="" src="http://gateoverflow.in/?qa=blob&qa_blobid=8333537619035037763"></p>Combinatoryhttps://gateoverflow.in/158148/%23-doubtSat, 07 Oct 2017 14:14:15 +0000kenneth rosen relations
https://gateoverflow.in/158028/kenneth-rosen-relations
How many of the 16 different relations on {0,1} contain the pair (0,1)?Combinatoryhttps://gateoverflow.in/158028/kenneth-rosen-relationsSat, 07 Oct 2017 07:01:40 +0000Inverse of a function
https://gateoverflow.in/158002/inverse-of-a-function
Consider a function f from A to B such that f : A → B is bijective.<br />
f–1 represents inverse of f.<br />
Than could we say that f-1 :B->A is also bijective..Please give proper reasoning thanksSet Theory & Algebrahttps://gateoverflow.in/158002/inverse-of-a-functionSat, 07 Oct 2017 05:50:01 +0000Preposition Logic: Verify the solution
https://gateoverflow.in/157896/preposition-logic-verify-the-solution
<p>Which of the following propositional statements is TRUE ?
<br>
<br>
A) ∀x ∀z ∃y [ P(x,y) ]---> ∃y ∀x ∀z [ P(x,y) ]
<br>
<br>
B) ∃y ∀x ∀z [ P(x,y) ]---> ∀x ∀z ∃y [ P(x,y) ]</p>
<p>I think in this</p>
<p>A) False </p>
<p>B) True</p>
<p>Explanation:-</p>
<p><strong>Domain :- Set of all negative numbers. {-inf to -1}</strong></p>
<p>P(x,y) --> x>=y;</p>
<p><strong>A) ∀x ∀z ∃y [ P(x,y) ]---> ∃y ∀x ∀z [ P(x,y) ]</strong></p>
<p><strong>Solving the LHS part </strong>:-</p>
<p>∀x ∀z ∃y [ P(x,y) ]</p>
<p>In this first we have to set the value of x then moving towards the value of y.</p>
<p>x = all value should satisfy the condition</p>
<p>y = x-1;</p>
<p>if x = -3, y = -4 Condition satisfied</p>
<p>if x = -1, y = -2 Condition satisfied.</p>
<p>As we can see for all value of x there exist a value y for which the condition is always holds true. So, LHS part is<strong> True.</strong></p>
<p>Moreover, LHS part always remain true because first we are setting the value of x, and then after setting x we can set y according always. hence it will always true.</p>
<p><strong>Solving the RHS part :-</strong></p>
<p>∃y ∀x ∀z [ P(x,y) ]</p>
<p>In this first we have to set the value of y then moving toward the value of x</p>
<p>y = -1, (Setting the value of y to -1)</p>
<p>x = all value should satisfy the condition</p>
<p>if y = -1, x = -1 Condition satisfied</p>
<p>if y = -1, x = -2 Condition not satisfied,</p>
<p>Since, The condition is not true for all value of x, Hence we can say that RHS part is <strong>false</strong> </p>
<p>Conclusion:-</p>
<p>By the rule of implication, True -> False = False</p>
<p>Hence, part A will be False,</p>
<p><strong>B) ∃y ∀x ∀z [ P(x,y) ]---> ∀x ∀z ∃y [ P(x,y) ]</strong></p>
<p>From the above explanation we can conclude that LHS part of this equation is false and RHS part is True.</p>
<p>By the rule of implication, False -> True = True</p>
<p>Finally conclude that:</p>
<p>A) False</p>
<p>B) True.</p>
<p>Let me know where it is going wrong.</p>Mathematical Logichttps://gateoverflow.in/157896/preposition-logic-verify-the-solutionFri, 06 Oct 2017 15:35:41 +0000Relations
https://gateoverflow.in/157250/relations
<p>Consider the set <em>S</em> = {<em>a</em>, <em>b</em>} and ‘<em>L</em>’ be a binary relation such that <em>L</em> = {all binary relations except reflexive relation set <em>S</em>}. The number of relation which are symmetric _______.</p>Set Theory & Algebrahttps://gateoverflow.in/157250/relationsWed, 04 Oct 2017 16:25:16 +0000Set theory
https://gateoverflow.in/157200/set-theory
<div>
<p>The number of pairs of set (<em>X</em>, <em>Y</em>) are there that satisfy the condition <em>X</em>, <em>Y</em> ⊆ {1, 2, 3, 4, 5, 6} and <em>X</em> ∩ <em>Y</em> = Φ ________.</p>
</div>
<div>
<ul>
</ul>
</div>Set Theory & Algebrahttps://gateoverflow.in/157200/set-theoryWed, 04 Oct 2017 12:24:38 +0000Set Theory and algebra
https://gateoverflow.in/157194/set-theory-and-algebra
<p>If we are given a set for ex.S={1,2,.....25} and now if we want to find subsets T ⊆ S of size 5 than it is 25C<sub>5</sub> or they are 2^ 25C<sub>5.</sub></p>Set Theory & Algebrahttps://gateoverflow.in/157194/set-theory-and-algebraWed, 04 Oct 2017 11:52:55 +0000set theory and algebra
https://gateoverflow.in/157037/set-theory-and-algebra
<p><img alt="" src="http://gateoverflow.in/?qa=blob&qa_blobid=7506087194220041859"></p>Set Theory & Algebrahttps://gateoverflow.in/157037/set-theory-and-algebraTue, 03 Oct 2017 17:09:38 +0000combinatorics
https://gateoverflow.in/157026/combinatorics
que- in how many way can 7 girl are seated at a round table so that 2 particular girl are seprated ???Combinatoryhttps://gateoverflow.in/157026/combinatoricsTue, 03 Oct 2017 16:55:04 +0000doubt
https://gateoverflow.in/157024/doubt
C intersection P(C) != phir ?why?<br />
<br />
(phi is subset of every set)???Mathematical Logichttps://gateoverflow.in/157024/doubtTue, 03 Oct 2017 16:53:21 +0000Can any one explain this question
https://gateoverflow.in/156771/can-any-one-explain-this-question
Consider the following first order logic formula in which R is a binary relation symbol.<br />
<br />
∀x∀y (R(x, y) => R(y, x))<br />
<br />
Only need to describe the question.@bikram sir.Mathematical Logichttps://gateoverflow.in/156771/can-any-one-explain-this-questionMon, 02 Oct 2017 15:32:34 +0000Group Theory
https://gateoverflow.in/156722/group-theory
<p>Let (G,<em>star) be a group such that for any a,b belongs to G, (a</em>b)power^71==(a)power^71 * (b)power^71, (ab)power^72==(a)power^72 * (b)power^72 and (ab)power^73=(a)power^73 * (b)power^73. Proove that G is Abelian Group.</p>Set Theory & Algebrahttps://gateoverflow.in/156722/group-theoryMon, 02 Oct 2017 10:56:28 +0000Asymmetric symmetric asymmetric difference?
https://gateoverflow.in/156657/asymmetric-symmetric-asymmetric-difference
What is meant by antisymmetric , asymmetric ? Any clear difference regarding symmetric, antisymmetric nd asymmetric regarding graph nd example?Mathematical Logichttps://gateoverflow.in/156657/asymmetric-symmetric-asymmetric-differenceMon, 02 Oct 2017 06:21:47 +0000gate previous
https://gateoverflow.in/156568/gate-previous
<p>The given explaination is almost fine.It will be more helpful to me if</p>
<p>someone give other example for this question (specially option d)</p>
<p><a rel="nofollow" href="http://gateoverflow.in/3783/gate2005-it-36">http://gateoverflow.in/3783/gate2005-it-36</a></p>Mathematical Logichttps://gateoverflow.in/156568/gate-previousSun, 01 Oct 2017 16:21:57 +0000GATE PREV
https://gateoverflow.in/156510/gate-prev
∃x(p(x)∧q(x))⟹(∃xp(x)∧∃xq(x))<br />
<br />
a)It is false because ∃ is not distributive over ∧<br />
<br />
b) If we say LHS is false ,then then entire statement is true.<br />
<br />
WHICH ONE I CHOOSE ?Mathematical Logichttps://gateoverflow.in/156510/gate-prevSun, 01 Oct 2017 10:53:23 +0000Discreet maths
https://gateoverflow.in/155926/discreet-maths
I am not able to find out any book for reading path walk close path......in a graph .<br />
<br />
And second group theory<br />
<br />
If anyone know about booksMathematical Logichttps://gateoverflow.in/155926/discreet-mathsThu, 28 Sep 2017 17:44:57 +0000GROUP-congruence classes
https://gateoverflow.in/155539/group-congruence-classes
<p>State true or false</p>
<p>1)Let n be an integer,The set Z<sub>n</sub> of congruence classes of integers n with respect to operation of addition is a GROUP.</p>
<p>2)The set Z<sub>n</sub>* of non-zero congruence classes modulo of n, with respect to the operation of multiplication is NOT a GROUP, where n is a prime number.</p>Mathematical Logichttps://gateoverflow.in/155539/group-congruence-classesWed, 27 Sep 2017 06:44:47 +0000Mathematical Logic question
https://gateoverflow.in/154332/mathematical-logic-question
<p><img alt="" src="http://gateoverflow.in/?qa=blob&qa_blobid=8700920070457993612"></p>
<p>Which among them are valid?</p>
<p>How to approach such questions ?</p>Mathematical Logichttps://gateoverflow.in/154332/mathematical-logic-questionFri, 22 Sep 2017 21:56:12 +0000Problem in linear algebra
https://gateoverflow.in/154297/problem-in-linear-algebra
How many solutions does the following system of linear equations have?<br />
<br />
X+5y = -1<br />
<br />
x-y = 2<br />
<br />
x+3y = 3 <br />
<br />
A. infinitely many<br />
<br />
B. two distinct solutions<br />
<br />
C. unique<br />
<br />
D. no solutionLinear Algebrahttps://gateoverflow.in/154297/problem-in-linear-algebraFri, 22 Sep 2017 17:09:39 +0000Preparation of Graph Theory
https://gateoverflow.in/154184/preparation-of-graph-theory
<p>Hello Sir, I have gone through the previous year questions and also gave some tests till now. From this experience I have realized that in <span class="marker"><strong>GRAPH THEORY - </strong></span><strong> almost 90% of the questions are theory based as a result I am not able to give the correct answer as I am not sure of the options in the given question. Hence whenever I see the question on Graphs Im simply skipping . Please provide some guidance and suggestions on how to get out of this situation and start understanding the subject answer the questions with confidence..</strong></p>
<p>Thank you</p>Study Resourceshttps://gateoverflow.in/154184/preparation-of-graph-theoryFri, 22 Sep 2017 08:21:37 +0000Problem in sets
https://gateoverflow.in/153321/problem-in-sets
<p><img alt="" src="http://gateoverflow.in/?qa=blob&qa_blobid=7932127215028874940"></p>
<p>more than 1 can be true or false </p>Set Theory & Algebrahttps://gateoverflow.in/153321/problem-in-setsTue, 19 Sep 2017 04:05:22 +0000Maths: functions: is given function bijective?
https://gateoverflow.in/153316/maths-functions-is-given-function-bijective
<p><strong>Question</strong> Determine whether the following function from R to R is a bijection
<br>
f(x) = $\frac{(x+1)}{(x+2)}$</p>
<p><strong>Solution:</strong>
<br>
First of all, this is not a function because f(-2) is not defined.</p>
<p>So, if the domain of the function is R - {-2} then this function is one-to-one.</p>
<p>And, if co-domain of this function is R - {1} then this function is onto.</p>
<p>So, the given function is bijection but with two above mentioned conditions. can someone please confirm?</p>
<p> </p>Set Theory & Algebrahttps://gateoverflow.in/153316/maths-functions-is-given-function-bijectiveTue, 19 Sep 2017 03:42:18 +0000sheldon M ross 4 ed - chapter-3 qno- 25
https://gateoverflow.in/153134/sheldon-m-ross-4-ed-chapter-3-qno-25
Fifty-two percent of the students at a certain college are females. Five percent<br />
of the students in this college are majoring in computer science. Two percent of<br />
the students are women majoring in computer science. If a student is selected at<br />
random, find the conditional probability that<br />
(a) this student is female, given that the student is majoring in computer science;<br />
(b) this student is majoring in computer science, given that the student is<br />
female.<br />
<br />
How to solve this qn by growing tree method?Probabilityhttps://gateoverflow.in/153134/sheldon-m-ross-4-ed-chapter-3-qno-25Mon, 18 Sep 2017 09:01:47 +0000Self doubt - Power Set
https://gateoverflow.in/153076/self-doubt-power-set
<p>Can you conclude A = B if A and B are 2 sets with the same power set ?
<br>
<br>
<strong>Doubt : Is power set of a set unique ?</strong></p>Set Theory & Algebrahttps://gateoverflow.in/153076/self-doubt-power-setMon, 18 Sep 2017 06:02:52 +0000Function Composition
https://gateoverflow.in/153066/function-composition
<blockquote>
<p><em><strong>For gof to be one-to-one, f must be one-to-one but reverse is not true.</strong></em></p>
</blockquote>
<p>Is the above statement correct?</p>
<p><strong>According to me both f and g must be one-to-one for gof to be one-to-one.</strong></p>
<p>I took below examples:</p>
<p>(i) f is one-to-one and g is onto</p>
<p>Let A = {1, 2, 3}, B = {a, b, c} and C = {α, β}.</p>
<p>Given f: A -> B where f(1) = a, f(2) = b, f(3) = c and g: B -> C where g(a) = α, g(b) = α, g(c) = β.</p>
<p>Then, gof: A -> C which gives g(f(1)) = g(a) = α, g(f(2)) = g(b) = α and g(f(3)) = g(c) = β.</p>
<p>Here, g(f(1)) and g(f(2)) both gives α which implies that <strong>gof is not one-to-one</strong>.</p>
<p> </p>
<p>(ii) f is onto and g is one-to-one</p>
<p>Let A = {1, 2, 3}, B = {a, b} and C = {α, β}.</p>
<p>Given f: A -> B where f(1) = a, f(2) = a, f(3) = b and g: B -> C where g(a) = α, g(b) = α.</p>
<p>Then, gof: A -> C which gives g(f(1)) = g(a) = α, g(f(2)) = g(a) = α and g(f(3)) = g(b) = β.</p>
<p>Here, also g(f(1)) and g(f(2)) both gives α which implies that <strong>gof is not one-to-one</strong>.</p>
<p> </p>
<p>(ii) f is one-to-one and g is one-to-one</p>
<p>Let A = {1, 2}, B = {a, b} and C = {α, β}.</p>
<p>Given f: A -> B where f(1) = a, f(2) = b and g: B -> C where g(a) = α, g(b) = α.</p>
<p>Then, gof: A -> C which gives g(f(1)) = g(a) = α and g(f(2)) = g(b) = β.</p>
<p>Here, g(f(1)) and g(f(2)) both gives α which implies that <strong>gof is one-to-one.</strong></p>
<p> </p>
<p>Are above examples correct? If yes, please explain.</p>Set Theory & Algebrahttps://gateoverflow.in/153066/function-compositionMon, 18 Sep 2017 05:31:28 +0000Propositional and First Order Logic GATE-CS-2006
https://gateoverflow.in/153032/propositional-and-first-order-logic-gate-cs-2006
In the question whether this statement is a tautology ((A ∨ B) → C)) ≡ ((A → C) ∨ (B → C)) ,<br />
<br />
If I take first part ((A ∨ B) → C)) as P and second part ((A → C) ∨ (B → C)) as Q , do I need to prove P-->Q is true? or both P-->Q and Q-->P as true? I am confused about the ≡ symbol.Mathematical Logichttps://gateoverflow.in/153032/propositional-and-first-order-logic-gate-cs-2006Sun, 17 Sep 2017 21:33:40 +0000PERMUTATIONS
https://gateoverflow.in/153020/permutations
<p><img alt="" src="http://gateoverflow.in/?qa=blob&qa_blobid=10393981935072026539"></p>Combinatoryhttps://gateoverflow.in/153020/permutationsSun, 17 Sep 2017 19:43:01 +0000Discrete Mathematics - Quantifiers problem
https://gateoverflow.in/151969/discrete-mathematics-quantifiers-problem
Establish these logical equivalences, where x does not occur as a free variable in A. Assume that the domain is nonempty.<br />
<br />
a) ∀x(A → P(x)) ≡ A → ∀xP(x)<br />
b) ∃x(A → P(x)) ≡ A → ∃xP(x)Mathematical Logichttps://gateoverflow.in/151969/discrete-mathematics-quantifiers-problemWed, 13 Sep 2017 20:01:38 +0000Propositional Logic
https://gateoverflow.in/151957/propositional-logic
<p>Can someone please check if my solution is correct?</p>
<p><img alt="" src="http://gateoverflow.in/?qa=blob&qa_blobid=13296924830599230077"></p>Mathematical Logichttps://gateoverflow.in/151957/propositional-logicWed, 13 Sep 2017 18:32:23 +0000Techhud
https://gateoverflow.in/151566/techhud
Find the total number of equivalent relations possible on a set S={4,7,1}?<br />
<br />
I am getting 8.Set Theory & Algebrahttps://gateoverflow.in/151566/techhudTue, 12 Sep 2017 08:16:02 +0000combinatorics
https://gateoverflow.in/151188/combinatorics
The number of even permutations of the multiset {1,1,2} is ___ .Combinatoryhttps://gateoverflow.in/151188/combinatoricsSun, 10 Sep 2017 12:12:02 +0000Probability
https://gateoverflow.in/151046/probability
If two fair coins are flipped and at least one of the outcomes is known to be a head, what is the probability that both outcomes are heads?<br />
<br />
Ans is 1/3.<br />
<br />
Why this answer does not come when we apply conditional probability?Mathematical Logichttps://gateoverflow.in/151046/probabilitySat, 09 Sep 2017 17:34:48 +0000Set theory doubt
https://gateoverflow.in/150080/set-theory-doubt
<h3>Say if A is proper subset of B i.e <strong>A⊂B </strong>then is it true - </h3>
<h3>that <strong>B⊆A</strong> (B is subset of A)?</h3>
<p>Also one more thing - if <strong>A⊂B then AUB = A where U means UNION</strong></p>Set Theory & Algebrahttps://gateoverflow.in/150080/set-theory-doubtTue, 05 Sep 2017 13:43:45 +0000madeEasy Q.4
https://gateoverflow.in/149582/madeeasy-q-4
Show that each of the conditional statement is a tautology<br />
not using a truth table<br />
<br />
$r\vee (p\vee q) is the conclusion from the premises (p \vee q) \wedge(q\rightarrow r)\wedge (p\rightarrow m) \wedge (m')$Mathematical Logichttps://gateoverflow.in/149582/madeeasy-q-4Sun, 03 Sep 2017 14:28:40 +0000Equivalence and Inverse of Relation.
https://gateoverflow.in/149325/equivalence-and-inverse-of-relation
Proof the following statement.<br />
<br />
1. If R1 and R2 are the equivalence relation on X then R1 $\cap$ $R2^{-1}$ (Inverse of R2) is also an equivalence relation.<br />
<br />
2. If R is reflexive and transitive relation on X then R $\cap$ $R^{-1}$ is an equivalence relation.Set Theory & Algebrahttps://gateoverflow.in/149325/equivalence-and-inverse-of-relationSat, 02 Sep 2017 15:36:34 +0000Discrete Mathematics practice ques
https://gateoverflow.in/148840/discrete-mathematics-practice-ques
<p><img alt="" src="http://gateoverflow.in/?qa=blob&qa_blobid=9991994797952680305"></p>
<p>provide negation of each of the statements</p>Mathematical Logichttps://gateoverflow.in/148840/discrete-mathematics-practice-quesThu, 31 Aug 2017 14:20:25 +0000relations
https://gateoverflow.in/147198/relations
what is the Number of relations S over set {0,1,2,3} such that (x,y) belongs to S=> x=ySet Theory & Algebrahttps://gateoverflow.in/147198/relationsFri, 25 Aug 2017 18:18:50 +0000Discrete_poset
https://gateoverflow.in/146192/discrete_poset
<p>It took me a while to solve, any hack on this?</p>
<p><img alt="" src="http://gateoverflow.in/?qa=blob&qa_blobid=12263858780788222777"></p>Set Theory & Algebrahttps://gateoverflow.in/146192/discrete_posetMon, 21 Aug 2017 17:36:38 +0000