Join Peggy Fisher for an indepth discussion in this video Solution: Practice with sets, part of Foundations of Programming: Discrete Mathematics.
 Now that you've had a chance to try the challenge,…let's go over a solution.…The first problem says what are the possible values…of n given this set notation.…The set of all values n that are elements…of the positive integers,…such that n is a factor of 8.…The only two numbers that are positive integers…and factors of eight are two and four.…Next, identify each of the following is true or false.…The set containing the number three is not an element…of the set on the right.…
So this is false.…The set on the left is a subset of the set on the right,…so the next one is true.…The set containing the number three…is an element of the set on the right…because this is a list of sets.…So this is going to be true.…And finally, the set on the left…containing just the number three…is not a subset of the set on the right…which is a set of sets.…So this is going to be false.…Next, for all sets A, B, and C,…we want to prove that A minus A intersects B…is equal to A minus B.…
We want to list the name of each law used.…We start with the equation on the left.…
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
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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

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Video: Solution: Practice with sets