Join Peggy Fisher for an indepth discussion in this video Evaluate conditional proofs, part of Foundations of Programming: Discrete Mathematics.
 [Voiceover] When evaluating conditional proofs…it's important to first review the definitions…in previously proven theorems related to number theory.…An integer n is even if, and only if…n equals twice some integer…written as n equals two k.…An integer n is odd if, and only if,…n equals twice some integer plus one,…written as n equals two k plus one.…An integer n is prime if, and only if,…n is greater than one…and for all positive integers r and s,…if n is equal to r times s,…then either r equals one or s equals one.…
In other words, n is prime as long as…n is only divisible by one and itself.…An integer n is called a perfect square…if, and only if, n equals k squared…for some integer k.…A real number r is considered rational…if, and only if, it can be expressed…as a quotient of two integers…with a nonzero denominator.…A previously proven theorem…says that the sum of any two rational numbers is rational.…
And finally, it's important to know…that integers are closed under addition,…subtraction and multiplication.…
Author
Peggy FisherReleased
3/9/2016This course relies on an opensource 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.
 Realworld 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

Welcome1m 11s


1. Discrete Math Uses

Realworld discrete math3m 8s

Abstract discrete math1m 57s

2. Sets

Objects as sets2m 56s

Set notation3m 56s

Set operations6m 30s

Power sets4m 33s

Sequences and sums7m 22s

Recursion3m 5s

Solution: Practice with sets6m 53s


3. Setting Up SML

Functional programming2m 31s

Datatypes4m 45s

Characters and strings5m 19s

Recursive functions4m 45s

Challenge: Learn SML1m 40s


4. Analyzing Data Sequences

Use SML to create lists4m 39s

Perform functions on lists4m 31s


5. Effective Arguments and Defensible Decisions

Truth tables4m 58s

Conditional propositions5m 47s

Valid arguments4m 40s

Rules of inference4m 46s

Prove logical equivalence6m 11s

Solution: Write truth tables4m 55s

6. Proofs Made Easy

Write subset proofs3m 12s

Evaluate conditional proofs8m 54s

Solution: Write a proof4m 24s

7. Advanced Discrete Math Topics

Event probability3m 31s

Cryptography2m 22s

Conclusion

Next steps35s

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Video: Evaluate conditional proofs