Join Peggy Fisher for an in-depth discussion in this video Solution: Write truth tables, part of Foundations of Programming: Discrete Mathematics.
- [Voiceover] In this challenge, you have to work…with truth tables, arguments and logically equivalences.…Let's take a look at my solution.…The first problem said, "Given the following statements,…"determine if they are logically equivalent…"using a truth table."…I have a truth table built with everything…except for one column.…Remember your mechanical form…when you fill in truth tables,…take the first column.…Fill in half with true and half with false.…After that, each column is going to be split in half again.…
All right, let's fill in this fourth column.…It says p or p and q.…So you wanna take a look at the values in p…and the values in p and q.…And then oral situation, true or true is true.…True or false is true.…False or false is false.…And false or false is false.…At this point, you'll compare those answers…to the value for just p…which I rewrote on the right hand side.…And since they're equal, that means these two statements…are logically equivalent.…
Let's take a look at a more complicated example.…Here's a much larger truth table…
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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