Join Peggy Fisher for an in-depth discussion in this video Rules of inference, part of Programming Foundations: Discrete Mathematics.
- [Voiceover] When evaluating arguments for validity,…there are several rules of inference that can…make the process much easier.…The idea is to take the original argument…and label each predicate with a unique variable.…Then rewrite the problem using the variables,…the logical connectors, and conditional statements…such as and, or, if then, not, et cetera.…Here's an example.…In this argument it says if it rains, Cy will be sick.…
Cy is not sick, therefore it did not rain.…Okay, let's label each predicate.…If it rains can be P.…Cy will be sick is going to be Q.…Cy is not sick will be not Q.…Therefore, it did not rain, not P.…Now I can say P then Q…for the first sentence.…That means if it rains, Cy will be sick.…The next premises or hypothesis is not Q,…meaning that Cy is not sick.…
Therefore, not P.…Now we can look at the rules of inference…to find a match to our format.…If we find a match, we know this is a valid argument.…Let's review the rules of inference.…The first one is modus ponens.…Modus ponens says if P then Q,…
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: Rules of inference