GATE Overflow - Recent questions in Discrete Mathematics
https://gateoverflow.in/questions/mathematics/discrete-mathematics
Powered by Question2AnswerFirst 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 +0000Counting
https://gateoverflow.in/161055/counting
Suppose that a person with 10 friends invites a different subset of 3 friends to dinner every night for 10 days. In how many ways can he do this so that all friends are included at least once ?<br />
<br />
How to approach this problem ?Mathematical Logichttps://gateoverflow.in/161055/countingWed, 18 Oct 2017 11:00:11 +0000Gate 2004| Logics| Let p,q,r, s be 4 primitive statements. Consider these arguments
https://gateoverflow.in/160578/gate-logics-primitive-statements-consider-these-arguments
<p>I tried solving this question using normal approach of writing the whole truth table and evaluating each proposition. This seems to be a very error-prone method. It took over 15-20 minutes. Is there any other method of solving this kind of questions? </p>
<p> </p>
<p><img alt="" src="https://gateoverflow.in/?qa=blob&qa_blobid=15990125441762074211"></p>Mathematical Logichttps://gateoverflow.in/160578/gate-logics-primitive-statements-consider-these-argumentsMon, 16 Oct 2017 16:14:27 +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 +0000P and C doubt
https://gateoverflow.in/159677/p-and-c-doubt
Given a 4 *4 grid points , how many Triangles with vertices on the grid can be formed?Combinatoryhttps://gateoverflow.in/159677/p-and-c-doubtFri, 13 Oct 2017 09:29:12 +0000P and C doubt
https://gateoverflow.in/159661/p-and-c-doubt
Number of ways in which the corner of the square can coloured with two colours.<br />
<br />
It is permissible to use single colour on all four corners?Combinatoryhttps://gateoverflow.in/159661/p-and-c-doubtFri, 13 Oct 2017 08:12:06 +0000P and C doubt
https://gateoverflow.in/159639/p-and-c-doubt
In how many ways can 10 different books be distributed to three students A B C so that student A receives at least one book?<br />
<br />
<br />
<br />
In how many ways can 10 different books be distributed to three students ?<br />
<br />
<br />
<br />
In how many ways can 10 different books be distributed to three students A B C so that each student receives at least 3 books?<br />
<br />
How to solve these types of questions...<br />
<br />
Any type of assistance would be appreciated..Combinatoryhttps://gateoverflow.in/159639/p-and-c-doubtFri, 13 Oct 2017 07:06:52 +0000Notes
https://gateoverflow.in/159638/notes
How many Simple non-isomorphic graphs are possible with vertices 9, edges 9, and degree of each vertex 2?<br />
<br />
an answer is given: 2<br />
<br />
please guide:<br />
<br />
But we can make 3<br />
<br />
1->a cyclic graph of 9 edge<br />
<br />
2-> two cycles one of 5 edge and other of 4 edge<br />
<br />
3-> three cycles of 3 edgeGraph Theoryhttps://gateoverflow.in/159638/notesFri, 13 Oct 2017 07:06:01 +0000logic
https://gateoverflow.in/159631/logic
prove<br />
<br />
((P=>Q)^(Q=>R))=>(P=>R) =1Mathematical Logichttps://gateoverflow.in/159631/logicFri, 13 Oct 2017 06:33:47 +0000#Numerical methods-syllabus
https://gateoverflow.in/159600/%23numerical-methods-syllabus
What is the syllabus for Engineering Mathematics - Numerical methods?Mathematical Logichttps://gateoverflow.in/159600/%23numerical-methods-syllabusFri, 13 Oct 2017 04:53:22 +0000number of solutions
https://gateoverflow.in/159595/number-of-solutions
When we find rank(A) and rank(AB)<br />
<br />
what are the cases to get<br />
<br />
1.no solution<br />
<br />
2.unique solution<br />
<br />
3.infinite solution<br />
<br />
4.more than one solutionMathematical Logichttps://gateoverflow.in/159595/number-of-solutionsFri, 13 Oct 2017 04:37:00 +0000Notes
https://gateoverflow.in/159591/notes
How many different (pairwise non-isomorphic trees are there of order 5)?Graph Theoryhttps://gateoverflow.in/159591/notesFri, 13 Oct 2017 04:19:20 +0000Rossen: How to perform Composition on Directed Graph.
https://gateoverflow.in/159587/rossen-how-to-perform-composition-on-directed-graph
<p>Given the directed graphs representing two relations, how can the directed graph of the union, intersection, symmetric difference, difference, and composition of these relations be found?</p>
<p>As, we can easily find, union, intersection, difference and symmetric difference. But how we can find composition of directed graph.</p>
<p>There is a ref:- <a rel="nofollow" href="https://math.stackexchange.com/questions/239897/draw-the-composition-of-directed-graphs">https://math.stackexchange.com/questions/239897/draw-the-composition-of-directed-graphs</a></p>
<p>But not explained clearly.</p>Set Theory & Algebrahttps://gateoverflow.in/159587/rossen-how-to-perform-composition-on-directed-graphFri, 13 Oct 2017 03:15:23 +0000GATE2001-2.15 GATE1994-1.6
https://gateoverflow.in/159550/gate2001-2-15-gate1994-1-6
<p>How many undirected graphs are possible with n vertices</p>
<ol style="list-style-type: lower-alpha;">
<li>if graphs are not necessarily connected</li>
<li>if they are necessarily connected</li>
</ol>
<p> </p>Graph Theoryhttps://gateoverflow.in/159550/gate2001-2-15-gate1994-1-6Thu, 12 Oct 2017 17:38:24 +0000UGCNET-Jan2017-III-60
https://gateoverflow.in/159508/ugcnet-jan2017-iii-60
The first order logic (FOL) statement ((R ∨ Q) ∧ (P ∨ ¬Q)) is equivalent to which of the following ?<br />
<br />
(1) ((R ∨ ¬Q) ∧ (P ∨ ¬Q) ∧ (R ∨ P))<br />
<br />
(2) ((R ∨ Q) ∧ (P ∨ ¬Q) ∧ (R ∨ P))<br />
<br />
(3) ((R ∨ Q) ∧ (P ∨ ¬Q) ∧ (R ∨ ¬P))<br />
<br />
(4) ((R ∨ Q) ∧ (P ∨ ¬Q) ∧ (¬R ∨ P))Mathematical Logichttps://gateoverflow.in/159508/ugcnet-jan2017-iii-60Thu, 12 Oct 2017 13:34:16 +0000UGCNET-Jan2017-III-59
https://gateoverflow.in/159507/ugcnet-jan2017-iii-59
<p>Which of the following statements is true ?</p>
<p>(1) The sentence S is a logical consequence of S<sub>1</sub>,…, S<sub>n</sub> if and only if S<sub>1</sub> ∧ S<sub>2</sub> ∧........ ∧ S<sub>n</sub> → S is satisfiable.</p>
<p>(2) The sentence S is a logical consequence of S<sub>1</sub>,…, S<sub>n</sub> if and only if S<sub>1</sub> ∧ S<sub>2</sub> ∧........ ∧ S<sub>n</sub> → S is valid.</p>
<p>(3) The sentence S is a logical consequence of S<sub>1</sub>,…, S<sub>n</sub> if and only if S<sub>1</sub> ∧ S<sub>2</sub> ∧........ ∧ S<sub>n</sub> ∧ ¬S is consistent.</p>
<p>(4) The sentence S is a logical consequence of S<sub>1</sub>,…, S<sub>n</sub> if and only if S<sub>1</sub> ∧ S<sub>2</sub> ∧........ ∧ S<sub>n</sub> ∧ S is inconsistent.</p>Mathematical Logichttps://gateoverflow.in/159507/ugcnet-jan2017-iii-59Thu, 12 Oct 2017 13:31:48 +0000Integration By Trapezoidal Rule (Gate 2014)
https://gateoverflow.in/159428/integration-by-trapezoidal-rule-gate-2014
Using the trapezoidal rule, and dividing the interval of integration into three equal subintervals, the definite integral ∫|x|dx is_______(Upper limit +1& Lower limit -1)Mathematical Logichttps://gateoverflow.in/159428/integration-by-trapezoidal-rule-gate-2014Thu, 12 Oct 2017 09:07:43 +0000schedule graph
https://gateoverflow.in/159384/schedule-graph
<p><img alt="" src="http://gateoverflow.in/?qa=blob&qa_blobid=15245219618812973391"></p>Graph Theoryhttps://gateoverflow.in/159384/schedule-graphThu, 12 Oct 2017 06:28:04 +0000boys and 4 girls have to sit in a row with all arrangements equally likely
https://gateoverflow.in/159364/boys-and-girls-have-sit-row-with-arrangements-equally-likely
3 boys and 4 girls have to sit in a row with all arrangements equally likely. What is the probability that no 2 boys sit next to each other<br />
<br />
a)1/7 b)2/7 c) 3/7 d)4/7Combinatoryhttps://gateoverflow.in/159364/boys-and-girls-have-sit-row-with-arrangements-equally-likelyThu, 12 Oct 2017 05:20:18 +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 +0000P & C doubt
https://gateoverflow.in/159265/p-%26-c-doubt
In how many Ways can 5 numbers be selected and arranged in ascending order from set 1 2 3 4 5 6 7 8 9 10?<br />
<br />
Ans. Is it 10C5 * 1ways<br />
<br />
Please correct me if I m wrong..Combinatoryhttps://gateoverflow.in/159265/p-%26-c-doubtWed, 11 Oct 2017 15:29:45 +0000graphs
https://gateoverflow.in/159198/graphs
[ D110 ; / ] = { 1,2,5,10,11,22,55,110} how are these values identifiedMathematical Logichttps://gateoverflow.in/159198/graphsWed, 11 Oct 2017 10:51:09 +0000P and C doubt
https://gateoverflow.in/159137/p-and-c-doubt
How many number must be chosen from site {1 2 3 4 5 6 7 8 }such that at least two of them must have sum equal to 9?<br />
<br />
A.28<br />
<br />
B.9<br />
<br />
C.5<br />
<br />
D.10Combinatoryhttps://gateoverflow.in/159137/p-and-c-doubtWed, 11 Oct 2017 05:22:55 +0000self_doubt #what is the meaning of this symbole
https://gateoverflow.in/159088/self_doubt-%23what-is-the-meaning-of-this-symbole
<p><img alt="" src="http://gateoverflow.in/?qa=blob&qa_blobid=8140142272456840399"></p>Mathematical Logichttps://gateoverflow.in/159088/self_doubt-%23what-is-the-meaning-of-this-symboleTue, 10 Oct 2017 19:20:36 +0000p'q'r is minterm of
https://gateoverflow.in/159039/pq-r-is-minterm-of
<p><img alt="" src="http://gateoverflow.in/?qa=blob&qa_blobid=17362700881302434138"></p>Mathematical Logichttps://gateoverflow.in/159039/pq-r-is-minterm-ofTue, 10 Oct 2017 16:13:54 +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 +0000propositional logic
https://gateoverflow.in/158918/propositional-logic
<p><strong>A) ((P->Q)->Q) ==> P V Q is given</strong></p>
<p><strong>How i solved</strong></p>
<p>((~P V Q)-->Q) </p>
<p>~(~P V Q) V Q</p>
<p>(P and ~Q) V Q</p>
<p>(P V Q) and ( ~Q VQ)</p>
<p>(P V Q) and Q</p>
<p>after this.. how to proceed?</p>
<p><strong>B) ( P <--> Q ) ==> (P and Q ) V ( ~p and ~Q)..............how ??</strong></p>
<p> </p>
<p> </p>Mathematical Logichttps://gateoverflow.in/158918/propositional-logicTue, 10 Oct 2017 06:33:55 +0000number of solutions
https://gateoverflow.in/158719/number-of-solutions
<h3>Number of non negative integer solutions such that x + y + z=17</h3>
<h3> where x>1 , y>2 , z>3</h3>
<p> </p>Mathematical Logichttps://gateoverflow.in/158719/number-of-solutionsMon, 09 Oct 2017 15:02:32 +0000rank of matrix
https://gateoverflow.in/158717/rank-of-matrix
A = 1 1 -1<br />
<br />
4 4 -3<br />
<br />
p 2 2<br />
<br />
Rank of matrix A is 2....find PMathematical Logichttps://gateoverflow.in/158717/rank-of-matrixMon, 09 Oct 2017 14:56:44 +0000Gate 2014 ME
https://gateoverflow.in/158633/gate-2014-me
If z is a complex variable, the value of ∫dz/z is____ { Upper limit = 3i & lower limit = 5}<br />
<br />
A. -0.511 - 1.57i<br />
<br />
B. -0.511 + 1.57i<br />
<br />
C. 0.511 - 1.57i<br />
<br />
D. 0.511 + 1.57iMathematical Logichttps://gateoverflow.in/158633/gate-2014-meMon, 09 Oct 2017 11:54:19 +0000Complex Function
https://gateoverflow.in/158630/complex-function
How to make a figure of<br />
<br />
|z - i| = 2.Mathematical Logichttps://gateoverflow.in/158630/complex-functionMon, 09 Oct 2017 11:41:20 +0000matrices
https://gateoverflow.in/158617/matrices
<p><img alt="" src="http://gateoverflow.in/?qa=blob&qa_blobid=7217952334567599098"></p>Mathematical Logichttps://gateoverflow.in/158617/matricesMon, 09 Oct 2017 10:45:55 +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 +0000he number of students who take both the subjects mathematics and chemistry is 30
https://gateoverflow.in/158530/number-students-take-subjects%C2%A0mathematics%C2%A0and-chemistry
The number of students who take both the subjects mathematics and chemistry is 30. This represents 10% of the enrolment in mathematics and 12% of the enrollment in Chemistry. How many students take atleast one of these two subjects?Set Theory & Algebrahttps://gateoverflow.in/158530/number-students-take-subjects%C2%A0mathematics%C2%A0and-chemistryMon, 09 Oct 2017 06:33:27 +0000discrete mathematics doubt .!
https://gateoverflow.in/158525/discrete-mathematics-doubt
What is the generating function for the sequence of Fibonacci numbers?Combinatoryhttps://gateoverflow.in/158525/discrete-mathematics-doubtMon, 09 Oct 2017 06:17:25 +0000UGCNET-Jan2017-II-5
https://gateoverflow.in/158418/ugcnet-jan2017-ii-5
Consider a Hamiltonian Graph G with no loops or parallel edges and with $|V(G)| = n ≥ 3$. Then which of the following is true ?<br />
<br />
(1) $deg(v) ≥ \frac{n}{2}$ for each vertex v.<br />
<br />
(2) $|E(G)| ≥ \frac{1}{2}(n – 1) (n – 2) + 2$<br />
<br />
(3) $deg (v) + deg(w) ≥ n$ whenever v and w are not connected by an edge.<br />
<br />
(4) All of the aboveGraph Theoryhttps://gateoverflow.in/158418/ugcnet-jan2017-ii-5Sun, 08 Oct 2017 21:11:38 +0000UGCNET-Jan2017-II-4
https://gateoverflow.in/158417/ugcnet-jan2017-ii-4
How many multiples of 6 are there between the following pairs of numbers ?<br />
<br />
0 and 100 and –6 and 34<br />
<br />
(1) 16 and 6<br />
<br />
(2) 17 and 6<br />
<br />
(3) 17 and 7<br />
<br />
(4) 16 and 7Combinatoryhttps://gateoverflow.in/158417/ugcnet-jan2017-ii-4Sun, 08 Oct 2017 21:07:34 +0000UGCNET-Jan2017-II-2
https://gateoverflow.in/158414/ugcnet-jan2017-ii-2
<p>Match the following :</p>
<p><strong>List – I List – II </strong></p>
<p>a. Absurd i. Clearly impossible being contrary to some evident truth.</p>
<p>b. Ambiguous ii. Capable of more than one interpretation or meaning.</p>
<p>c. Axiom iii. An assertion that is accepted and used without a proof.</p>
<p>d. Conjecture iv. An opinion preferably based on some experience or wisdom.</p>
<p><strong>Codes : </strong></p>
<p> a b c d</p>
<p>(1) i ii iii iv</p>
<p>(2) i iii iv ii</p>
<p>(3) ii iii iv i</p>
<p>(4) ii i iii iv </p>Mathematical Logichttps://gateoverflow.in/158414/ugcnet-jan2017-ii-2Sun, 08 Oct 2017 20:53:40 +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 +0000Narsing Deo--Graph theory
https://gateoverflow.in/158248/narsing-deo-graph-theory
<pre>
<code>Show that every planar graph with at least 4 vertices has at least 4
vertices of degree less than or equal to 5.This will also prove there is no 6-connected planar graph.</code></pre>
<p><code>I have proved it partly,can someone please give provide a simple proof to this,especially the 2nd part.</code></p>
<p>Also one doubt,</p>
<p>Sum of degrees of a vertices in graph we know is = 2* no of edges.</p>
<p>Now, Sum of regions of graph (region in terms of graph planarity) is also 2* no of edges.</p>
<p>Is there a interconnection between these terms no just in terms of formula?Can we use it interchangebly.</p>
<p> </p>Graph Theoryhttps://gateoverflow.in/158248/narsing-deo-graph-theorySun, 08 Oct 2017 08:26:43 +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 +0000combinatory
https://gateoverflow.in/158141/combinatory
Consider all possible permutations of eight distinct elements a, b, c, d, e, f, g, h. In how many of them, will d appear before b? Note that d and b may not necessarily be consecutive.Combinatoryhttps://gateoverflow.in/158141/combinatorySat, 07 Oct 2017 13:59:40 +0000mathematics
https://gateoverflow.in/158062/mathematics
the number of integers n with 100<n<200 such that 8 divides (n^2-n-2) and 27 divides (n^2+2n-3)Mathematical Logichttps://gateoverflow.in/158062/mathematicsSat, 07 Oct 2017 10:13:10 +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 +0000testbook test series
https://gateoverflow.in/158006/testbook-test-series
<p><strong>number of string of length 3 using 4 distinct alphabet...</strong></p>
<p><strong>including string of length zero and what if dont.? </strong></p>
<p> </p>Combinatoryhttps://gateoverflow.in/158006/testbook-test-seriesSat, 07 Oct 2017 06:02:38 +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 +00002008 previous question with answers on propositional logic
https://gateoverflow.in/157475/2008-previous-question-with-answers-on-propositional-logic
Mathematical Logichttps://gateoverflow.in/157475/2008-previous-question-with-answers-on-propositional-logicThu, 05 Oct 2017 09:18:51 +0000