Recent questions tagged discrete-maths - GATE CSE Doubts

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Kenneth H. Rosen 7th edition
Show that ¬(p ⊕ q) and p ↔ q are logically equivalent.

asked 6 days ago in Mathematical Logic by Champa (5 points) | 5 views

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Discrete Mathematics and its applications (Kenneth Rosen)

asked Mar 22 in Mathematical Logic by SmeetPatel (5 points) | 18 views

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Kenneth H Rosen
Show that $p<-->q$ and ~p <-->~q are logically equivalent.

asked Mar 20 in Mathematical Logic by ShivangiChauhan (17 points) | 17 views

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Kenneth H Rosen
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 by ShivangiChauhan (17 points) | 16 views

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GATE functions and relations
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 by donniedarko (39 points) | 34 views

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Dominating set and Independent set.
Please explain the basic difference between Independent set and Dominating Set?

asked Feb 21 in Graph Theory by arpit_18 (5 points) | 16 views

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SELF DOUBT IN IMPLICATIONS
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 ... <--> q If p is neither sufficient nor necessary is the same as ! (p <--> q)

asked Feb 9 in Mathematical Logic by s_dr_13 (15 points) | 18 views

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NPTEL Assignment
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 by Kindaichi (10 points) | 23 views

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Ace Test Series
Is the group closed under monoid? Can we treat 1 as identity??

asked Feb 3 in Mathematical Logic by vipin.gautam1906 (9 points) | 24 views

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Kenneth H rosen Chapter 6 - "Counting" Section 6.4

asked Jan 20 in Combinatory by ykrishnay (7 points) | 17 views

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Lattice self doubt
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 by tusharSingh (5 points) | 7 views

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Gate overflow book
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)? ... 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 by hadarsh (5 points) | 19 views

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What is total number of planer graph can be formed with 6 vertices ?

asked Jan 11 in Graph Theory by subhadip997 (9 points) | 38 views

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TestBook Test Series
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 by nisargdoshi (7 points) | 43 views

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Made easy 2018 postal study course
Why is the answer is d)? I guess it should be a) can someone explain please

asked Dec 28, 2020 in Mathematical Logic by Anshul purohit (5 points) | 21 views

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how to prove function injective or not
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 by tyagiabhi (5 points) | 20 views

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#made-easy #discrete-maths
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 by 404 found (37 points) | 13 views

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#self-doubt #discrete-maths
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. ... 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 by 404 found (37 points) | 19 views

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#dicrete-maths #made-easy
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 by 404 found (37 points) | 18 views

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#discrete-maths #made-easy
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 ... 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 by 404 found (37 points) | 10 views

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#discrete-maths #made-easy
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 by 404 found (37 points) | 12 views

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Kenneth H Rosen
What is the meaning of all the four options? Please explain in detail.

asked Nov 27, 2020 in Mathematical Logic by Kindaichi (10 points) | 38 views

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Could not found the source
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 by Marwa-jami (5 points) | 25 views

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Kenneth h rosen 7th Edition chapter 2 section 2.5 "cardinality of sets"

asked Nov 21, 2020 in Set Theory & Algebra by ykrishnay (7 points) | 27 views

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Kenneth h rosen 7th Edition chapter 2 section 2.4 "Sequences and Summation"

asked Nov 20, 2020 in Set Theory & Algebra by ykrishnay (7 points) | 23 views

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A site on google
Which of the following formulas represents the sentence, 'Share prices will go up, and if interest rates go up too, there will be a recession', where; p means 'share prices will go up' q means 'interest rates will go up' r means 'there will be a recession'. A) (p ∧ q) →r B) p∧( q →r)

asked Nov 17, 2020 in Mathematical Logic by Marwa-jami (5 points) | 19 views

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BS Gerewal engineering mathematics
hey guys, what is meant by the statement- “cards are drawn in succession” . does it means whether one by one the cards were drawn OR all the cards were drawn at once any help is really appreciated….

asked Oct 29, 2020 in Probability by rish1602 (9 points) | 17 views

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Gatebook function
How to solve this type of question ?

asked Oct 2, 2020 in Set Theory & Algebra by Raj_81 (23 points) | 23 views

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NPTEL DISCRETE STRUCTURE ASSIGNMENT QUESTION
Which of the following are logical consequences of { ($\alpha$ → $\beta$’), $\beta$, ($\gamma$ ’ → $\alpha$) } ($\alpha$ → $\beta$’) $\beta$’ $\gamma$ $\alpha$ Answer given is C but if this question asked as MSQ question then can A be the possible answer??

asked Sep 19, 2020 in Mathematical Logic by Akanksha Agrawal (309 points) | 69 views

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Self doubt - Graph Connectivity (NPTEL & PY)
Let G be a graph with n vertices and if every vertex has a degree of at least $\frac{n−1}{2}$ then G is connected. Source : https://gateoverflow.in/1221/gate2007-23 Let G be a graph with n vertices and if every vertex has a degree of at ... then G is connected. source : https://nptel.ac.in/courses/106/106/106106183/ My doubt : Which one is right?

asked Sep 17, 2020 in Graph Theory by KUSHAGRA गुप्ता (1.4k points) | 54 views

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Self Doubt - Planar graph (PY)
$K_5$ is non-planar. I am showing you my proof. Please tell me whether this is the right way or not to prove that $K_5$ is non-planar. $\sum$ (deg)$=4+4+4+4+4=20$ $e=10$ and $n=5$ Assume $K_5$ is planar. $v-e+r=2$ ... $K_5$ is non-planar. If this is the right way, why this method didn't work in this graph. Source: https://gateoverflow.in/87129/gate1990-3-vi

asked Sep 15, 2020 in Graph Theory by KUSHAGRA गुप्ता (1.4k points) | 36 views

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KENNETH ROSEN DISCRETE MATHEMATICS PAGE 432 Q11
How many ways are there to chose eight coins from piggy bank containing 100 identical pennies and 80 identical nickels.

asked Sep 14, 2020 in Combinatory by ijnuhb (747 points) | 93 views

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LATTICE ASSOCIATIVITY DOUBT
I wasn't convinced about the associativity property of lattices, and the proof i found on math.stackexchange seemed reasonable, but still i couldnt wrap my head around it. I tried to make a counter example, and in the above diagram (b join c) ... otherwise it would've satisfied associativity. But i cant seem to figure out why this diagram isn't a lattice. Please help.

asked Aug 22, 2020 in Set Theory & Algebra by rish-18 (9 points) | 64 views

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Self Doubt in Propositional Logic
Translate this English proposition to Logical expression : “you will not get an A grade unless you work hard”

asked Aug 21, 2020 in Mathematical Logic by AbhayPrajapati (7 points) | 39 views

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ISI CSB 2018
State, with justification, which of the following expressions f, g and h, define valid real-valued functions over the set of positive rational numbers. We denote a rational number by m/n, where m and n are positive integers. (a) f(m/n) = 2^m − 2^n. (b) g(m/n) = log m − log n. (c) h(m/n) = (m^2 − n^2)/(mn).

asked Aug 20, 2020 in Set Theory & Algebra by suparna kar (9 points) | 32 views

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K Rosen(7th ed). Chapter 6. Exercise 6.4. Q.17.
Question: Answer 1: Answer 2: I am not able to understand the solution.What’s happening here? Please help.

asked Aug 13, 2020 in Combinatory by RasMalai (27 points) | 31 views

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Self-Doubt 10 couple, { 10 men and 10 women }, Number of Ways

asked Aug 12, 2020 in Combinatory by mamtuj (-25 points) | 59 views

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ISI CSB 2018
Given A = {1, 2, 3, .... , 70}, show that for any six elements a1, a2, a3, a4, a5 and a6 belonging to A, there exists one pair ai and aj for which |ai − aj| ≤ 14 (i not equals to j).

asked Aug 11, 2020 in Set Theory & Algebra by suparna kar (9 points) | 34 views

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Combinatorics and Probability
Six people, including A,B, and C, form a queue in a random order (all 6! orderings are equiprobable). Consider the event "B is between A and C in the queue". What is its probability? (The order of A and C can be arbitrary, but B should be between them).

asked Aug 5, 2020 in Probability by aryashah2k (2 points) | 35 views

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Combinatorics and Probability
Six people including A,B, and C, form a queue in a random order (all 6! orderings are equiprobable). Consider the event "A precedes B in the queue". (Again this event does not mention C or other people in the queue. It happens when A is ... not require that B is the next after A, some people could be between A and B.) What is the probability of this event?

asked Aug 5, 2020 in Probability by aryashah2k (2 points) | 323 views

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