Join Peggy Fisher for an in-depth discussion in this video Solution: Practice with sets, part of Programming Foundations: 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.…
This course relies on an open-source 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.
- Real-world 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
1. Discrete Math Uses
3. Setting Up SML
4. Analyzing Data Sequences
5. Effective Arguments and Defensible Decisions
6. Proofs Made Easy
7. Advanced Discrete Math Topics
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