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Cheatography

Discrete Math Exam Part 2 Cheat Sheet (DRAFT) by

This is a draft cheat sheet. It is a work in progress and is not finished yet.

Predicates and Quantified Statements

Universal
∀x ∈ D, P(x)
∃x∈ D, ~P(x)
Existe­ntial
∃(x,y)∈ D,x≠y|­P(x,y)
∀(x,y)∈ D,x≠y|­~P(x,y)
Universal Condit­ional
∀x, P(x)→Q(x)
∃x∈ D|P(x)­∧~Q(x)
~exist­ential = universal
~universal = existe­ntial

More Formal Statements

Formal Contra­pos­itive
∀x ∈ D, Q(x)→P(x)
Formal Converse
Q(x)→P(x) ∀x ∈ D
Formal Inverse
∀x ∈ D, P(x)→Q(x)
 

MQ Invalid Arguments

Quantified Converse
∀x, P(x)→Q(x)
 
Q(j) for a particular j
 
∴P(j)
Quantified Inverse Error
∀x, P(x)→Q(x)
 
~P(j) for a particular j
 
∴~Q(j)

Multiple Quanti­fiers

Existe­ntial MQ
∃x ∈ D|∀y ∈ E, P(x, y)
Neg. MQ
∀x ∈ D, ∃y ∈ E | P(x, y) [original]
∃x ∈ D, ∀y ∈ E | ~P(x, y) [negation]
Universal Modes Pones
 
∀x ∈ Z, P(x)→Q(x)
   
P(k), for a particular k ∈ Z
   
∴ ~Q(k)
Universal Modus Tones
 
∀x ∈ D, P(x)→Q(x)
   
~Q(j), j ∈ D
   
∴ ~P(j)