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Recent questions tagged discrete-mathematics

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Kenneth Rosen Edition 6th Exercise 6.6 Question 3 (Page No. 456)
How many solution does the equation x1+x2+x3=13 have where x1 x2 and x3 are non negative less than 6 ?
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Need of Concept Clarity
I want to understand Validity Check in First order logic. Also I want to have technique or specific way of how to approach or answer GATE question on this ... Answer. It would be great help for GATE aspirants like me.Thanks in Advance.
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Doubt
A $\phi$ (empty) relation on any set $A$ is not reflexive because for every $ a \in A$, $(a, a) \notin \phi$, but $\phi$ is a symmetric as well as transitive relation on $A$, how is that possible $?$
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Kenneth Rosen Edition 6th Exercise 5.5 Question 44 b (Page No. 381)
. In how many ways can a dozen books be placed on four distinguishable shelvesif no two books are the same, and the positions of the books on the shelves matter?
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Find chromatic number and matching number of a graph
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Find the number of into functions
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Kenneth Rosen Edition 6th Exercise 5.2 Example 4 (Page No. 348)
show that for evry n there is a multiple of n such that its decimal expansion has only 0's and 1's.
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General Topic Doubt Set Theory & Algebra: Groups
In the above question my doubt is instead of under multiplication if we change under ADDITION then what is its value?plz someone explain details.
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Combinatorics
A proffesor writes 40 discrete mathematics true/false question . of the statements in these question 17 are true . if the question can be positioned in any order . then how many diff key are possible ?
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DMGT question
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UGC NET CSE | August 2016 | Part 3 | Question: 74
Consider the following logical inferences :$I_{1}$ ... $I_{1}$ and $I_{2}$ are not correct inferences.
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UGC NET CSE | August 2016 | Part 3 | Question: 70
Let $ν(x)$ mean $x$ is a vegetarian, $m(y)$ for $y$ is meat, and $e(x, y)$ for $x$ eats $y$. Based on these, consider the following sentences : ... .Only $I$ and $III$ are equivalent sentence .$I, II,$ and $III$ are equivalent sentences.
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NET 2015 Paper 2
How many solutions are there for the equation $x+y+z+u=29,\, x\geq 1,y\geq 2,z\geq 3,u\geq 0$ ?
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Expectated no of coin toss
An unbiased coin is tossed repeatedly and outcomes are recorded. What is the expected no of toss to get HT ( one head and one tail consecutively) ?
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UGC NET CSE | August 2016 | Part 2 | Question: 3
Let $A$ and $B$ be sets in a finite universal set $U$. Given the following : $|A - B|, |A \bigoplus B|, |A| + |B|$ and $|A \cup B|$ Which of the following is in order of ... $|A - B| < |A \bigoplus B| < |A \cup B| < |A| + |B|$
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UGC NET CSE | August 2016 | Part 2 | Question: 2
Let us assume that you construct ordered tree to represent the compound proposition $(\sim (p \wedge q)) \leftrightarrow (\sim p \vee \sim q)$.Then, the prefix expression ...
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UGC NET CSE | August 2016 | Part 2 | Question: 1
The Boolean function $[\sim (\sim p \wedge q)\wedge \sim(\sim p \wedge \sim q)] \vee (p \wedge r)$ is equal to the Boolean function :$q$p \wedge r$p \vee q$ $p$
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counting
How many team of six with a captain can be selected from 12 person?
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Kenneth Rosen Edition 6th Exercise 1.3 Question 25 a,b (Page No. 48)
Anyone plz explain the difference between-"No one is perfect.""Not everyone is perfect."How to translate the above statements into logical expressions using predicates,quantifiers and logical connectives..Thnx in advance..
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MadeEasy Test Series: Combinatory - Permutations And Combinations
Number of 10 bit binary string where the string contains 3 consecutive 0's or 3 consecutive 1's?
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Probability Distribution
In the cartesian plane, selection of a point P along the y axis in [0,2] is uniformly random. Similarly selection of a point Q along the x axis in [0,2] also ... of the triangle POQ to be less than or equal to 1, where O is the origin ?
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UGC NET CSE | December 2010 | Part 2 | Question: 3
A partially ordered set is said to be a lattice if every two elements in the set haveA unique least upper boundA unique greatest lower boundBoth $(A)$ and $(B)$None of the above
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Counting
How many ways are there to seat six people around a circular table where two seatings are considered the samewhen everyone has the same two neighbors without ... or left neighbors?It would be better if one provide a pictorial explanation.
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UGC NET CSE | June 2011 | Part 2 | Question: 3
The proposition $\sim p \vee q$ is equivalent to$p \rightarrow q$ $q \rightarrow p$p \leftrightarrow q$ $p \vee q$
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Counting Theory
10 Points were selected in the sequence with each side 1 unit, there will be atleast two points (of those points) such that distance between them can not exceeds..1/(2.sqrt(2))(sqrt(2))/31/3(sqrt(2))/9
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Counting Theory
5 points were selected in an equilateral triangle with each side 1 units. There will at least 2 points (of those points) such that the distance between them can not exceed 1/21/31/4None
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Validity of an implication based on a given implication
If the proposition $\lnot p \to q$ is true, then the truth value of the proposition $\lnot p \lor \left ( p \to q \right )$, where ... negation,$\lor$ is inclusive OR and $\to$ is implication, isTrueMultiple ValuesFalseCannot be determined
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UGC NET CSE | December 2011 | Part 2 | Question: 43
The proposition $\sim$ qvp is equivalent top $\rightarrow$ q q $\rightarrow$ p p $\leftrightarrow$ q p $\vee$ q
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Kenneth Rosen: Counting-Chapter 5
How many license plates consisting of three letters followed by three digits contain no letter or digit twice?
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UGC NET CSE | December 2011 | Part 2 | Question: 34
Negative numbers cannot be represented inSigned magnitude form$1’s$ complement form$2’s$ complement formNone of the above
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