Join Peggy Fisher for an indepth discussion in this video Set operations, part of Foundations of Programming: Discrete Mathematics.
 [Voiceover] Now that we've defined a set…and reviewed the set notation,…we can move on to Set Operations.…In the Exercises file, there is a folder…that contains several reference materials,…including a list of all the set operations…and laws used in this movie.…Use that as a reference…when you try the challenge for this section.…In set theory, we'll use the following operations:…Set Intersection.…It's written as A intersects B…and the formal notation says…that the result of the intersection of sets A and B…is the set of all values X such that…X is an element of A,…and X is an element of B.…
Set Union is A union B.…And this definition says…the set of all values X,…where X is an element of A,…or X is an element of B,…or both.…Next, we have Set Difference,…which takes the elements in set A…minus the elements in set B.…The formal definition says…the set of all values X…such that X is an element of A,…and X is not an element of B.…
Set Complement.…Set Complement is written as A with a line over it,…or A raised to the C power.…
Author
Peggy FisherReleased
3/9/2016This course relies on an opensource SML (standard machine language) library to demo the concepts behind discrete math. Peggy Fisher shows you how to manipulate sets of data, write proofs and truth tables, analyze data sequences, and visualize data using graph theory. Challenges at the end of every chapter allow you to test your knowledge. By the end of the course, you should be able to make the leap from theory to using discrete math in practice: saving time and resulting in code that's cleaner and easier to maintain in the long run.
 Realworld discrete math
 Objects as sets
 Set notation and operations
 Standard machine language (SML) setup
 Working with data types, strings, and functions in SML
 Analyzing data sequences
 Writing truth tables
 Identifying and evaluating predicates
 Validating arguments
 Writing proofs: subset, conditional, and biconditional proofs
 Visualizing data with graphs
 Advanced discrete math techniques
Skill Level Intermediate
Duration
Views
Related Courses

Foundations of Programming: Design Patterns
with Elisabeth Robson2h 19m Intermediate 
Code Clinic: C++
with Bill Weinman2h 4m Intermediate 
Everyday Math Fundamentals
with Vince Kotchian2h 6m Appropriate for all

Introduction

Welcome1m 11s


1. Discrete Math Uses

Realworld discrete math3m 8s

Abstract discrete math1m 57s

2. Sets

Objects as sets2m 56s

Set notation3m 56s

Set operations6m 30s

Power sets4m 33s

Sequences and sums7m 22s

Recursion3m 5s

Solution: Practice with sets6m 53s


3. Setting Up SML

Functional programming2m 31s

Datatypes4m 45s

Characters and strings5m 19s

Recursive functions4m 45s

Challenge: Learn SML1m 40s


4. Analyzing Data Sequences

Use SML to create lists4m 39s

Perform functions on lists4m 31s


5. Effective Arguments and Defensible Decisions

Truth tables4m 58s

Conditional propositions5m 47s

Valid arguments4m 40s

Rules of inference4m 46s

Prove logical equivalence6m 11s

Solution: Write truth tables4m 55s

6. Proofs Made Easy

Write subset proofs3m 12s

Evaluate conditional proofs8m 54s

Solution: Write a proof4m 24s

7. Advanced Discrete Math Topics

Event probability3m 31s

Cryptography2m 22s

Conclusion

Next steps35s

 Mark as unwatched
 Mark all as unwatched
Are you sure you want to mark all the videos in this course as unwatched?
This will not affect your course history, your reports, or your certificates of completion for this course.
CancelTake notes with your new membership!
Type in the entry box, then click Enter to save your note.
1:30Press on any video thumbnail to jump immediately to the timecode shown.
Notes are saved with you account but can also be exported as plain text, MS Word, PDF, Google Doc, or Evernote.
Share this video
Embed this video
Video: Set operations