Preface
How to approach this topic, what to learn
+
Sets
Like a list, but no order or repeats
+
Examples
From real life and mathematics
+
+
Sets Representation
Roster and builder forms
+
+
Classification By Size
Empty, finite, and infinite
+
+
+
Common Number Sets
+
+
+
+
Sets!
Collecting all from Sets
+
Interrelations
Sets ⬌ Sets ⬌ Elements
+
Membership
a ∈ B
+
Subset Superset Equality
A ⊂ B; B ⊃ A; A = B
+
+
Intervals
(a, b) and other variants
+
+
Power Set
P(A)
+
+
Universal Set
U
+
+
+
+
Venn Diagrams
Visualization
+
+
Operations
Similar to addition, subtraction, etc; but for sets
+
Union
A ∪ B
+
Intersection
A ∩ B
+
Difference
A - B
+
Complement
A′
+
Cardinality
n(A) or |A|
+
Cartesian Product
A X B
+
+
+
+
Operations!
+
Operator Properties
+
Commutative
p + q = q + p
+
Associative
(p + q) + r = p + (q + r)
+
Identity
p x 1 = p
+
Idempotent
p & p = p
+
Distributive
p x (q + r) = p x q + p x r
+
Conversion*
Converts everything to a special value (*made up name)
+
De Morgan's Law
(a & b)' = a' | b'
+
+
Cardinality After Operations
Cardinality after operations like union, intersection, etc
+
+
+
+
+
+
+
Operator Properties!
+
+
Relations
Subset of A X B
+
Image Domain Range
+
+
Functions
f : A → B
+
Common Functions
Identity, Constant, Polynomial, Rational