Sets
1 hr 28 min 23 Examples
- Overview of Set Notation, Roster Method and Set-builder notation
- Determine if the sets are equal, equivalent, both or neither (Examples #1-4)
- Write each set using either roster method or set builder notation (Examples #5-10)
- Overview of Universal Set, Empty Set, Subset and Proper Subset
- Are the pair of sets equal? (Examples #11-17)
- Determine which are subsets (Examples #18-19)
- True/False for elements, subsets and proper subsets (Example #20a-l)
- Intro to Cardinality and Power Sets
- What is the cardinal number of each set? (Example #21a-f)
- Find the power set and determine its cardinality (Example #22a-c)
- Explanation of n-tuple and Cartesian Product
- Discover the cartesian product (Example #23a-f)
Set Operations
1 hr 34 min 9 Examples
- Overview of Union, Intersection, Disjoint, Pairwise Disjoint, Complement, Difference of Sets, and Symmetric Difference
- Explanation of the Principle of Inclusion-Exclusion
- Draw a Venn diagram and perform the set operations (Example #1a-g)
- Create a Venn diagram and use PIE to draw conclusions (Example #2a-c)
- Shade the correct solution in a Venn Diagram (Example #3a-h)
- Representing sets as bit strings (Examples #4a-g)
- How to Partition a set (Examples #5-6)
- Minset Defined (Examples #7-9)
Set Identities
1 hr 39 min 14 Examples
- Properties of Subsets, Universal and Empty Sets, and Set Identities
- Proving set identities using Venn Diagrams (Example #1)
- Prove set properties by membership table (Examples #2a-b)
- Using set theory to prove set relations (Examples #3-6)
- Use the element method to verify set relations (Examples #7-8)
- Verify each set identity (Examples #9-10)
- Prove each set identity (Examples #11-14)
Chapter Test
38 min 15 Practice Problems
- Perform the following set operations (Problems #1-9)
- Draw and shade a Venn Diagram (Problem #10a-c)
- Find the Cartesian Product (Problem #11a-b)
- Is the following a subset or an element? (Problem #12a-b)
- Results from a survey (Problem #13)
- Use a direct proof to show set relation (Problem #14)
- Prove set equality (Problem #15)