# Recent questions tagged discrete-mathematics

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How to prove the following statement is valid with the help of Inference Rules? (P $\wedge$ ( P $\rightarrow$ Q) ) $\rightarrow$ ($\sim$ Q $\vee$ P)
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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 .....
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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)
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answer given is 27 how to approach these kind of questions? what forulas will be used here?
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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?
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(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
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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
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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
1 vote
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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
1 vote
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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
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#Discrete-Mathematics: whether Binomial Theorem is part of the syllabus?
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We select 38 even positive integers, all less than 1000. Prove that therewill be two of them whose difference is at most 26.
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(a). Use Fermat's little theorem to compute 52003 (mod 7), 52003(mod 11) and 52003(mod 13)
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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)
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Show that ¬(p ⊕ q) and p ↔ q are logically equivalent.
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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.
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is section 7.2 n-ary relations and their applications given in kenneth rosen included or important for gate preparation??
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Show that $p<-->q$ and ~p <-->~q are logically equivalent.
1 vote
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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)
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
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Please explain the basic difference between Independent set and Dominating Set?
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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)
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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?
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Is the group closed under monoid? Can we treat 1 as identity??
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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
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Establish relationship between semi lattice, lattice, bounded lattice, finite lattice, complement lattice, distribute lattice and Boolean algebra. [ Using Venn Diagram ]
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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
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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
0 answers 25 views
Why is the answer is d)? I guess it should be a) can someone explain please
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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.
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
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?
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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?
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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).
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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?