Join Peggy Fisher for an in-depth discussion in this video Power sets, part of Foundations of Programming: Discrete Mathematics.
- [Voiceover] Next let's talk about power sets.…A power set is the set of all subsets…for a particular set including the empty set.…The cardinality of a power set…is two to the n, where n is the cardinality…of the original set.…For example, if the cardinality of set A…is equal to three, which means that A has three elements,…then the cardinality of the power set of A,…which is denoted with a script P…in front of the A, is equal to eight,…because two-cubed is equal to eight.…
All right, if we're given the set…A equals the set containing one, two, and three,…let's write the power set of A.…So we know, since there's three items,…there's going to be eight sets.…I'll start with the empty set so I don't forget that one.…And this is going to be a set of sets.…Next, I'll do each individual number.…A set containing one,…two, three.…
Now I'll start to do combinations of two.…One and two.…I definitely need to include a set that has…all the original elements, and I think I'm done.…If we count them we have one, two, three,…four, five, six, seven, and eight.…
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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