- [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,…
Author
Peggy Fisher
Released
3/9/2016This 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
Duration
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Introduction
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Welcome1m 11s
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1. Discrete Math Uses
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Real-world discrete math3m 8s
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Abstract discrete math1m 57s
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2. Sets
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Objects as sets2m 56s
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Set notation3m 56s
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Set operations5m 1s
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Power sets4m 29s
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Sequences and sums7m 22s
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Recursion3m 5s
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Solution: Practice with sets6m 53s
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3. Setting Up SML
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Functional programming2m 31s
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Datatypes4m 45s
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Characters and strings5m 19s
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Recursive functions4m 45s
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Challenge: Learn SML1m 40s
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4. Analyzing Data Sequences
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Use SML to create lists4m 39s
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Perform functions on lists4m 31s
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5. Effective Arguments and Defensible Decisions
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Truth tables4m 58s
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Conditional propositions5m 48s
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Valid arguments4m 40s
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Rules of inference4m 45s
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Prove logical equivalence6m 11s
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Solution: Write truth tables4m 55s
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6. Proofs Made Easy
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Write subset proofs3m 12s
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Evaluate conditional proofs8m 54s
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Solution: Write a proof4m 23s
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7. Advanced Discrete Math Topics
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Event probability3m 31s
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Cryptography2m 22s
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Conclusion
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Next steps35s
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Video: Truth tables