Join Peggy Fisher for an in-depth discussion in this video Truth tables, part of Programming Foundations: Discrete Mathematics.
- [Voiceover] To evaluate complex statements,…it's often helpful to use truth tables.…Truth tables provide a visual representation…of the sentence, using variables for each proposition…and operators for any logical connectors…such as and, or, but, nor.…Let's start with a very simple example of a truth table.…This truth table only has two values, p and not p.…So the two values for p are either T for true…or F for false.…
Not in front of the variable changes the value…true to false…and false to true.…Okay, let's look at a more complicated truth table.…Here's two truth tables.…On the left, I have two variables, p and q,…representing propositions,…and the question is, what happens when I evaluate p or q?…On the right, the same two variables,…and I'm going to evaluate p and q.…We'll start by filling in the table on the left.…
We'll start with p as…true, true, false, false.…Now, I'll fill in the q values.…This time, I'll alternate.…True, false, true, false.…Now, p or q.…True or true is true.…As long as one of the statements is true,…
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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