## Mathematical Proofs

###### A variety of examples related to sets are worked.  We learn/define basic set notation; do examples with set operations such as union, intersection, and complements; and use Venn diagrams to visualize different set relationships and establish several set identities.

Sets Example 01

3/11/14

Running Time: 7:07

Given a set written using an elementhood test, we explicitly list all elements of the set between braces, {}.  Several different examples are provided.

Sets Example 02

3/11/14

Running Time: 6:20

Given a set whose elements have been listed explicitly between braces, {}, we compactly write the set using an elementhood test.  Several different examples are provided.

Sets Example 03

3/12/14

Running Time: 4:40

We work with the sets A = {all prime numbers}, B = {1, 2, 10, 17, 25}, and C = {2, 11, 20, 42}.  The main goal of this example is to demonstrate basic set operations (e.g. set union, set intersection, and set difference) by performing several simple computations.

Sets Example 04

3/12/14

Running Time: 6:08

We practice constructing and using Venn diagrams in this example.  Sequences of Venn diagrams are used to verify that two sets are indeed equal to each other.  Two different set equality examples are worked.

Sets Example 05

3/12/14

Running Time: 8:09

The same sets as investigated in Proof and Problem Solving - Sets Example 04 are also examined here.  However, instead of establishing set equality using Venn diagrams, we use logical symbols and basic definitions to verify equivalence.