Join Peggy Fisher for an in-depth discussion in this video Valid arguments, part of Programming Foundations: Discrete Mathematics.
- [Voiceover] In discrete math, it's important…to understand what makes a valid argument.…An argument consists of a sequence…of propositions, called hypotheses.…They're followed by a final proposition,…called the conclusion.…All propositions are either true or false.…But when dealing with arguments,…it's important to note that an argument…is either valid or invalid.…Let's take a look at determining argument validity.…An argument is valid if the conclusion is true…whenever all the hypotheses are true.…
Otherwise, it's considered invalid.…An argument form contains one or more hypotheses…and one conclusion, usually written in this format:…proposition one, proposition two,…all the way down to proposition n,…and at the n we'll have three dots…which represents therefore, see our conclusion.…So in this case, p1, p2, to pn…all have to be true at the same time…the conclusion is true, then the argument is valid.…
Otherwise, it's invalid.…Let's take a look at a sample argument.…In this case, we have Today is Monday.…That's a proposition that's either true or false.…
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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