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Lecture on set theory relations covering power sets, Cartesian products, binary relations, and equivalence relations. Focus on reflexive, symmetric, and transitive properties leading to set division concept.

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At-a-glance checklist

• [ ] Review power set definition and examples
• [ ] Practice union, intersection, and difference operations
• [ ] Understand ordered pairs and Cartesian products
• [ ] Master binary relation examples with tables and diagrams
• [ ] Learn reflexive, symmetric, and transitive properties
• [ ] Study equivalence relations and equivalence classes
• [ ] Understand set division through equivalence relations
• [ ] Work through clock arithmetic (mod 12) example
• [ ] Practice divisibility by 3 example

Core concepts covered

Power sets

• Power set P(A) is the set of all possible subsets of A
• Example: If A = {man, dog}, then P(A) = {∅, {man}, {dog}, {man, dog}}
• Includes the empty set and the full set itself
• Each element can either be included or excluded

Set operations

• Union (A ∪ B): All elements in A or B
• Intersection (A ∩ B): Only elements in both A and B