Discrete Mathematics Lecture 1 Logic of Compound Statements
Alexander Bukharovich New York University
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Rosen, Discrete Mathematics and Its Applications, 6th edition
Extra Examples
Section 9.3Representing Graphs and Graph Isomorphism
Page references correspond to locations of Extra Examples icons in the textbook.
p.616, icon at Example 9
Relations
Chapter Summary
Relations and Their Properties
n-ary Relations and Their Applications
Representing Relations
Closures of Relations (not currently included in
overheads)
Equivalence Relations
Partial Orderings
Relations and Their Properties
Bi
Propositional Logic
# Is the following sentence a proposition? If it is a proposition, determine
whether it is true or false.
Portland is the capital of Maine.
# Is the following sentence a proposition? If it is a proposition, determine
whether it is true
This is the submission by
Sahil Shah (netid :sbs554@nyu.edu N Number : N12706992)
FCS Homework 3
1. Determine whether the following graphs are isomorphic.
Soln:
Here the number of vertices and number of edges are same which are 6 and 10 respectively so
th
This is the submission by
Sahil Shah (netid :sbs554@nyu.edu N Number : N12706992)
Dhruv Amin (netid: dva227@nyu.edu N Number: N11713617 )
Poojan Shah (netid : pss382@nyu.edu N Number : N10482975)
FCS Homework 1
Problem #1
The following proposition uses th
This is the submission by
Sahil Shah (netid :sbs554@nyu.edu N Number : N12706992)
FCS Homework 2
1.
Use the definition of big-O to prove that
Ans. Let us assume x > 1 .
To prove that the given function is big-O of
For x > k .
Since
This leads to
Where cor
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Alexander Bukharovich New York University
Graphs
Graph consists of two sets: set V of vertices and set E of edges. Terminology: endpoints of the edge, loop edges, parallel edges, adjacent vertices, isolated vertex, subgraph
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Recursive Sequences
A recurrence relation for a sequence a0, a1, a2, is a formula that relates each term ak to certain collection of its predecessors. Each recurrence sequence needs
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Alexander Bukharovich New York University
Generic Functions
A function f: X Y is a relationship between elements of X to elements of Y, when each element from X is related to a unique element from Y X is called domain of f,
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Counting and Probability
Coin tossing Random process Sample space is the set of all possible outcomes of a random process. An event is a subset of a sample space Probability of an e
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Basics of Set Theory
Set and element are undefined notions in the set theory and are taken for granted Set notation: cfw_1, 2, 3, cfw_1, 2, cfw_3, cfw_1, 2, 3, cfw_1, 2, 3, , , cfw_
Discrete Mathematics
Lecture 4: Sequences
and Mathematical Induction
Alexander Bukharovich
New York University
Sequences
Sequence is a set of (usually infinite number of)
ordered elements: a1, a2, , an,
Each individual element ak is called a term, wher
Discrete Mathematics
Lecture 3
Elementary Number Theory and
Methods of Proof
Alexander Bukharovich
New York University
Proof and Counterexample
Discovery and proof
Even and odd numbers
number n from Z is called even if k Z, n = 2k
number n from Z is c
Discrete Mathematics
Lecture 2
Logic of Quantified Statements
Alexander Bukharovich
New York University
Predicates
A predicate is a sentence that contains a
finite number of variables and becomes a
statement when specific values are
substituted for the v
Show All Solutions
Rosen, Discrete Mathematics and Its Applications, 6th edition
Extra Examples
Section 9.5Euler and Hamilton Paths
Page references correspond to locations of Extra Examples icons in the textbook.
p.634, icon at Example 2
#1. Determine wh