Sect 2a. Elementary Set Theory

CONCEPTS

Set, element, membership
Notation: N, Z, Q, +, *, -
Containing: subset, superset, equality
Powerset, cardinality
Combining: intersection, union, complement, different, symmetric difference
Properties: associativity, commutativity, distributivity, absorpion
Venn diagrams

Notation: indexing, generalized union and intersection
Partitioning
Cartesian product, multiset, multiset union and intersection

SKILLS
  
  1. Identify concepts in a context
     E.g., what are the elements of {1,{2},3}
     E.g., is 2 an element of {1,{2},3}
  2. Evaluate set expressions
     E.g., let A={1,2,3} and B={3,4,5}, what is A intersect B
     E.g., if (A difference B) = A, for sets A and B, what can you say about B
     E.g., compute union and intersection of multisets
     E.g., tell whether a set is/is not a partion of another
  3. Prove/disprove simple statements
     E.g., Prove that (A intersect B) union A = A
     E.g., Disprove that (A union B) is contained in B
  
SOURCES

  *** Recommended ***   
  Tutorialspoint: Discrete Mathematics - Sets (simple)
  https://www.tutorialspoint.com/discrete_mathematics/discrete_mathematics_sets.htm

  *** Recommended ***   
  Wikibooks: Discrete Mathematics/Set theory (lots of exercises)
  https://en.wikibooks.org/wiki/Discrete_Mathematics/Set_theory
  
  Wikibooks: Discrete Mathematics/Naive set theory (partial)
  https://en.wikibooks.org/wiki/Discrete_Mathematics/Naive_set_theory

  Wikibooks: Set Theory/Sets (partial)
  https://en.wikibooks.org/wiki/Set_Theory/Sets

  Youtube: Discrete Math 1, Introduction to Sets by TheTrevTutor, videos 1-9.
  https://www.youtube.com/watch?v=5plFb4jrzd4&list=PLDDGPdw7e6Ag1EIznZ-m-qXu4XX3A0cIz

  Slideshare: Sets by Abdur Rehman Usmani (gentle introduction)
  https://www.slideshare.net/AbdurRehmanUsmani1/sets-55548178

  *** Recommended ***   
  Lerma, sect 2.1

  LLM, sect 4.1

  Hammack, chap 1 (!!! lots of examples and exercises !!!)