Join Peggy Fisher for an in-depth discussion in this video Understand biconditional proofs, part of Programming Foundations: Discrete Mathematics.
- [Voiceover] Biconditional proofs…Biconditional statements are written…as p with a double arrow q.…When you see that,…it means p, if and only if, q.…The biconditional statement is true…when both p and q have the same truth value…and false if they are different.…That is not the same as saying…that both p and q are true.…In reality, if p and q are both true,…then the biconditional statement is true,…but if p and q are both false,…it is still true.…
The only time that a biconditional statement is false…is when they don't match:…p is true, q is false…or p is false and q is true.…Another way to state a biconditional statement…is p is necessary and sufficient for q.…Finally, I want to point out…that a biconditional statement…is logically equivalent to the two conditional statements…joined by an and sign,…if p then q and if q then p.…
For this proof, I'm going to use sets.…This proof states that the difference…between sets A and B is equal to the empty set…if and only if A is a subset of B.…Again, we start the proof by saying suppose.…
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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