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Welcome to GATE CSE Doubts, where you can ask questions and receive answers from other members of the community.

Recent questions tagged discrete-mathematics

0 votes
1 answer 10 views
How to prove the following statement is valid with the help of Inference Rules? (P $\wedge$ ( P $\rightarrow$ Q) ) $\rightarrow$ ($\sim$ Q $\vee$ P)
asked Jul 27 in Mathematical Logic ShivangiChauhan 17 points 10 views
0 votes
1 answer 161 views
linear-algebra .. 1. https://gateoverflow.in/questions/mathematics/linear-algebra 2. https://gatecse.in/linear-algebra/ 3. https://gateoverflow.in/tag/determinants 4. https://gateoverflow.in/tag/system-of-equations 5. https://gateoverflow.in/tag/system-of-equations? ... . Finding values by Mean Value Theorem. Integration.... https://drive.google.com/file/d/0Byt7-j-JD0d0bmxlRkZGcjN2cjA/view .....
asked Jul 20 in GATE asqwer 633 points 161 views
0 votes
1 answer 19 views
A tree has 14 vertices of degree 1 and degree of each of remaining vertices is 4 or 5. If the tree has ‘n’ vertices then number of vertices with degree 5 is:- (40-2n) (3n-54) (54-2n) (3n-40)
asked Jul 14 in Graph Theory subhashchaganti 5 points 19 views
0 votes
1 answer 13 views
answer given is 27 how to approach these kind of questions? what forulas will be used here?
asked Jul 10 in Mathematical Logic Sharma9999999 5 points 13 views
0 votes
1 answer 17 views
Find the eigenvalues and the eigenvectors of these two matrices: A = \begin{bmatrix}1&4\\2&3\end{bmatrix} and A+I = \begin{bmatrix}2&4\\2&4\end{bmatrix} A+I has the eigenvectors _____ as A. Its eigenvalues are ______ by 1. I have computed the eigen values please help me in determining a relation between them. Is there any formula or theorem I’m missing out on?
asked Jul 10 in Linear Algebra kirtipurohit 15 points 17 views
0 votes
1 answer 24 views
(G,*) is an abelian group .Then, (i). $X$ =$X^{-1}$ for any X belonging to G. (ii). $X$=$X^{2}$ for any X belonging to G. (iii). $(X*Y)^{2}$ = $X^{2}$ * $Y^{2}$ for any X ,Y belonging to G. (iv). G is of finite order
asked Jul 4 in Set Theory & Algebra ShivangiChauhan 17 points 24 views
0 votes
1 answer 11 views
N denotes the set of natural numbers,{0,1,2,3 .} ,Z denotes the integers { ..-2,-2,0,1,2, ...} Which of the following statements are true ? (i). For all p $\epsilon$ Z ,p>5 $\rightarrow$ There exists x $\epsilon$ N,$x^{2}$ = 1(mod p). (ii). If m is any natural number satisfying m ... x. (a). only (i) is true (b). only (ii) is true ( c). both (i) and (ii) are true (d). both (i) and (ii) are false
asked Jul 4 in Set Theory & Algebra ShivangiChauhan 17 points 11 views
0 votes
1 answer 20 views
Hi There is 2 book for graph theory so which book is followed because is rosen is short for graph theory and deo is very detailed so for gate which book is followed ? in rosen so there is complete detail for graph theory so if i read rosen so can i make gate related questions or not ? thank you
asked Jun 30 in Graph Theory ykrishnay 103 points 20 views
1 vote
0 answers 18 views
A chair car compartment has 16 chairs in a row and 12 people randomly take up a chair each and the next person comes up with additional luggage which requires him to have two adjacent chairs. The probability that the 13th person is able to sit on the same row is ? A) 11/20 B) 4/7 C) 81/140 D) 17/28
asked Jun 26 in Mathematical Logic Dheeraj Varma 19 points 18 views
1 vote
1 answer 131 views
A multiple-choice test contains 10 questions. There are four possible answers for each question. In how many ways can a student answer the questions on the test if the student answers every question? In how many ways can a student answer the questions on the test ... there is no mention of it in question whether we should consider the order in which questions are solved or not? Thanks in advance
asked May 24 in Combinatory ssap09 21 points 131 views
0 votes
0 answers 19 views
#Discrete-Mathematics: whether Binomial Theorem is part of the syllabus?
asked May 10 in Combinatory Parag Tamhankar 5 points 19 views
0 votes
0 answers 13 views
We select 38 even positive integers, all less than 1000. Prove that therewill be two of them whose difference is at most 26.
asked May 6 in Combinatory thispc295 5 points 13 views
0 votes
0 answers 14 views
(a). Use Fermat's little theorem to compute 52003 (mod 7), 52003(mod 11) and 52003(mod 13)
asked May 6 in Engineering Mathematics Mushy 5 points 14 views
0 votes
0 answers 22 views
Find the number of paths of length n between any two nonadjacent vertices in K3,3 for the following values of n: a)2 b)3. c)4. d)5 ( i am able to understand the number of paths of length n between any two adjacent vertices in K3,3… but i am not able to get intuition for non adjacent in the adjacency matrix)
asked Apr 26 in Graph Theory ami_c05 5 points 22 views
0 votes
0 answers 20 views
Show that ¬(p ⊕ q) and p ↔ q are logically equivalent.
asked Apr 7 in Mathematical Logic Champa 5 points 20 views
0 votes
0 answers 5 views
I've a personal doubt X^2 doesn't have an inverse but cubic function is bijective because it's derivative is square term and hence always positive. I am confused about these two things in theoritically.
asked Apr 5 in Set Theory & Algebra afroze 7 points 5 views
0 votes
0 answers 26 views
is section 7.2 n-ary relations and their applications given in kenneth rosen included or important for gate preparation??
asked Mar 22 in Mathematical Logic SmeetPatel 5 points 26 views
0 votes
1 answer 50 views
Show that $p<-->q$ and ~p <-->~q are logically equivalent.
asked Mar 20 in Mathematical Logic ShivangiChauhan 17 points 50 views
1 vote
1 answer 48 views
Let p and q be propositions p: I bought a lottery ticket this week q: I won the million-dollar jackpot Express each of these propositions as English sentences (i) ~p (ii) p$\vee$q (iii) p$\rightarrow$q (iv) p$\wedge$q (v) p$\Leftrightarrow$q (vi) ~p$\rightarrow$~q (vii) ~p$\wedge$~q (viii) ~p$\vee$(p$\wedge$q)
asked Mar 20 in Mathematical Logic ShivangiChauhan 17 points 48 views
1 vote
0 answers 43 views
The function f: [0,3]$\rightarrow$[1,29] defined by f(x) = $2x^{3} - 15x^{2} + 36x +1$ where x is an integer is (a) injective and surjective (b) surjective but not injective (C) injective but not surjective (d) neither injective not surjective
asked Mar 7 in Mathematical Logic donniedarko 39 points 43 views
0 votes
1 answer 30 views
Please explain the basic difference between Independent set and Dominating Set?
asked Feb 21 in Graph Theory arpit_18 5 points 30 views
0 votes
0 answers 22 views
Can anybody please make me understand what's the relationship among implications in proposition logic and statements such as 1. Necessarily but not sufficient 2. Sufficient but not necessary 3. Sufficient as well as necessary 4. Neither sufficient nor necessary ( although I am skeptical about this specific ... is same as p <--> q If p is neither sufficient nor necessary is the same as ! (p <--> q)
asked Feb 9 in Mathematical Logic s_dr_13 15 points 22 views
0 votes
0 answers 28 views
In how many ways can one arrange five 1’s and five -1’s so that all ten partial sums (starting with the first summand) are nonnegative?
asked Feb 6 in Combinatory Kindaichi 10 points 28 views
0 votes
0 answers 31 views
Is the group closed under monoid? Can we treat 1 as identity??
asked Feb 3 in Mathematical Logic vipin.gautam1906 9 points 31 views
0 votes
0 answers 23 views
Hi I have a doubt regarding a topic “Binomial coeffiecients and identities” so my doubt is, this topic is important for gate or not, means i study this section “Binomial coeffiecients and identities” of chapter 6 in Rosen book for gate or any questions will be asked from this section previously gate exams. Thank you
asked Jan 20 in Combinatory ykrishnay 103 points 23 views
0 votes
0 answers 9 views
Establish relationship between semi lattice, lattice, bounded lattice, finite lattice, complement lattice, distribute lattice and Boolean algebra. [ Using Venn Diagram ]
asked Jan 18 in Set Theory & Algebra tusharSingh 5 points 9 views
0 votes
0 answers 24 views
I am having a confusion in precedence order of logical operators. For e.g. consider the expression (a ∧ b) → (a ∧ c) ∨ d. Then how is the expression evaluated? Like is it ((a ∧ b) → (a ∧ c)) ∨ d or (a ∧ b) →((a ∧ c) ∨ d)? I read ... precedence than implication, so the second one should be correct. But from the solution, I see it is the first one. Link to the question: https://gateoverflow.in/654
asked Jan 16 in Mathematical Logic hadarsh 5 points 24 views
0 votes
1 answer 47 views
Consider G(V, E) be a complete undirected graph with 6 edges having a distinct weight from 1, 3, 9, 27, 81, and 243. Which of the following will NOT be the weight of them minimum spanning tree of G? (*This question may have multiple correct answers) A)121 B)13 C)40 D)31
asked Jan 1 in Graph Theory nisargdoshi 7 points 47 views
0 votes
0 answers 25 views
Why is the answer is d)? I guess it should be a) can someone explain please
asked Dec 28, 2020 in Mathematical Logic Anshul purohit 5 points 25 views
0 votes
0 answers 24 views
Let A, B, and C be finite sets, and f : B to C and g : A to B be functions. Let h be the function with domain A and range C that maps x in A to f (g(x)). Prove or disprove the following claim: If h is injective, then g must be injective.
asked Dec 21, 2020 in Set Theory & Algebra tyagiabhi 5 points 24 views
0 votes
0 answers 16 views
A group of 5 friends sitting on a bench. You have joined them with 8 sweets.All of you decided to share among ourself. The number of ways this distribution is possible is ___ i am getting ans 1287 but answer given is 20160 my approach is distribution of undistinguishable objects into distinguishable boxes. so formula is n+r-1Cr here n =6,r=8 so ans is 13C8
asked Dec 9, 2020 in Combinatory 404 found 37 points 16 views
0 votes
1 answer 25 views
can someone explains difference between equivalence classes and partitions. according to wiki Every element x of X is a member of the equivalence class [x]. Every two equivalence classes [x] and [y] are either equal or disjoint. Therefore, the set of ... but in below gate question https://gateoverflow.in/652/gate2000-2-5 they considers equivalence classes as partitions.Can someone explains why?
asked Nov 30, 2020 in Set Theory & Algebra 404 found 37 points 25 views
0 votes
1 answer 20 views
Let G be a group.Suppose that the number of elements in G of order 5 is 28.Determine the number of distinct subgroups of G of order 5 __. Ans -7 .can someone explains how?
asked Nov 28, 2020 in Set Theory & Algebra 404 found 37 points 20 views
0 votes
0 answers 12 views
In a poset (A,<=) ,if there is no element ,x belongs to A with x<y then which of the following is true? An element x exists for which x=y. An element x is maximal in poset. A set with the same subset of poset An element x is minimal in poset. Ans is b ... think it is correct bcz an element x is said to maximal if there exists no element y belongs to A such that xRy holds (x<y in this question).
asked Nov 28, 2020 in Set Theory & Algebra 404 found 37 points 12 views
0 votes
0 answers 14 views
For sets A and B ,let f:A?B and g:B?A be functions such that f(g(x))=x for each x.which of the following options is/are true? The function f must be one to one. The function f must be onto The function g must be one to one the function g must be onto ans is b,c. can someone explains how?
asked Nov 28, 2020 in Set Theory & Algebra 404 found 37 points 14 views
0 votes
1 answer 44 views
What is the meaning of all the four options? Please explain in detail.
asked Nov 27, 2020 in Mathematical Logic Kindaichi 10 points 44 views
0 votes
0 answers 27 views
A)T B) F C) T D) F E) T F) T G) F H) T Are these truth values that I assigned correct?
asked Nov 21, 2020 in Mathematical Logic Marwa-jami 5 points 27 views
0 votes
1 answer 34 views
is it necessary to read cardinality of sets section and it is important from gate point of view ?
asked Nov 21, 2020 in Set Theory & Algebra ykrishnay 103 points 34 views
0 votes
0 answers 30 views
The “Sequences and summations” section in chapter 2 is in gate syllabus or not and is it necessary to read this section for next chapters like counting etc or this section is used in later chapters or not according to gate syllabus ? thank you
asked Nov 20, 2020 in Set Theory & Algebra ykrishnay 103 points 30 views
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