Sample Problems in Discrete Mathematics This handout lists some sample problems that you should be able to solve as a pre-requisite to Design and Analysis of Algorithms Try to solve all of them You should also read Chapters 2 and 3 of the textbook and look at the Exercises at the end of these chapters
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Solutions: 1 Yes A= B We will prove this by showing that A Band B A We begin by showing that A B Let a2A then we know that a= 2k for some integer k Letting k = j 1 where j is an integer we see that a= 2(j 1) = 2j 2 so a2B hence A B Now we show B A Let b2B This means that b= 2j 2 for some integer j
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Discrete Maths: Exercises and Solutions
Discrete Maths: Exercises and Solutions Basic Structures: Sets Functions Sequences Sums and Matrices Basic Structures: Sets Functions Sequences Sums and Matrices Much of discrete mathematics is devoted to the study of discrete structures used to represent discrete objects
How do you identify a sequence in discrete mathematics?
Identifying a sequence when the first few terms are provided is a useful skill when solving problems in discrete mathematics. Definition: A sequence is a function from a subset of the set of integers (usually either the set {0, 1, 2, . . .} or the set {1, 2, 3, . . .}) to a set S.
What is continuous mathematics based on?
Continuous Mathematics is based on a continuous number line or real numbers in continuous form. It is defined by the fact that there is virtually always an endless quantity of numbers between any two integers. In continuous Mathematics, for example, a function can be depicted as a smooth curve with no breaks.
Why are graphs important in discrete mathematics?
Graphs are one of the most important objects of study in Discrete Mathematics. Discrete Mathematics and graph theory are complementary to each other. Graphs are present everywhere. They are models of structures either made by man or nature. They can model various types of relations and process dynamics in physical, biological and social systems.
What is discrete mathematics?
The field of mathematics known as discrete mathematics is concerned with the study of discrete mathematical structure. There are two different types of data: discrete and continuous. Instead of studying continuous data, discrete mathematics examines discrete data. Finite mathematics is another name for it.
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