Join Peggy Fisher for an in-depth discussion in this video Prove logical equivalence, part of Programming Foundations: Discrete Mathematics.
- Logical equivalences.…Although two statements might…have very different semantic meaning,…such as, dogs bark and cats meow,…this can actually be logically equivalent to,…the sky is blue and the grass is green.…At first, this might sound absurd.…But the reality is that both statements,…on either side of the and operator,…are true.…So the overall statement is true.…And if the overall statements match,…in this case, both true,…then they are considered logically equivalent.…
Using p and q to denote two separate statements,…if they are logically equivalent,…we can use this special symbol.…P is logically equivalent to q.…Remember, the semantic meaning…of the sentence is not in question.…Only the logical form of the statements.…Truth tables are used to determine logical equivalence.…By using the canonical form,…we can easily determine if the conclusions match,…without reordering the rows.…
To prove that two statement forms…are not logically equivalent,…we only need to find one row that is different.…Okay, let's take a look at an example.…
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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