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PM 1001 - Sets and Combinatorics (Set Theory (set operations (union and…
PM 1001 - Sets and Combinatorics
Methods of Proofs
algebra of propositions
Distributive Laws
Identity Laws
Commutative Laws
Complement Laws
Associative Laws
Involution Law
Idempotent Laws
De Morgan's Laws
propositional functions and quantifiers
basic logic operations / connectives
NOT
IF...THEN
OR
IF and only IF (IFF)
AND
how to prove?
indirect proof
counter example
contrapositive
contradiction
Fundamental Theorem of Arithmetic
direct proof
induction
PSMI
Well Ordering Principle
PMI
proof by cases
rules of logic
Set Theory
Venn diagrams
set operations
union and intersection
compliments
subsets
algebra of sets
universal set
finite and infinite sets
empty set
categorical propositions and syllogisms
Russel's paradox
arbitrary unions and intersections
sets
collections of sets
power sets
partitions
Cartesian product
Combinatorics
Generating Functions
calculating coefficients of generating functions
integer partitions
generating function models
exponential generating functions
Pigeon Hole Principle
General Counting Methods
arrangements and selections with repetitions
distributions (r objects in n boxes)
simple arrangements and selections
binomial coefficients
two basic principles
addition principle
multiplication principle