Introduction to Logic Exam 2
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When does p → q come out false?
 Only when p is true and q is false
 (When p is false, it comes out true regardless of what q is)

When does pVq come out false?
 Only when both p and q are false
 (When p is true, it comes out true regardless of what q is)

How do you find validity in a truth table?
 It's valid if it's always true
 It's invalid if at least one thing comes out false

How do you do the invalidity shortcut method?
 1. Start with the conclusion if there's only one way to make the conclusion false
 OR
 Start with the premises if there's more than one way to make the conclusion false
 2. Make the conjunction turn into T→F form

What does Modus Ponens (MP) look like?

What does Modus Tollens (MT) look like?

What does Absorption (Abs) look like?

What does Disjunction Syllogism (DS) look like?

What does Hypothetical Syllogism (HS) look like?

What does Simplification (Simp) look like?

What does Conjunction (Conj) look like?

What does Addition (Add) look like?

What does Constructive Dilemma (CD) look like?

What does Commutation (Comm) look like?

What does Association (Assoc) look like?
 (pV(qVr))↔((pVq)Vr)
 OR
 (p⋅(q⋅r)↔((p⋅q)⋅r)

What does De Morgan's Law (DeM) look like?
 (pVq)↔(p⋅q)
 OR
 (p⋅q)↔(pVq)

What does Implication (Imp) look like?
(p→q)↔(pVq)

What does Transposition (Trans) look like?
(p→q)↔(q→p)

What does Equivalence (Equiv) look like?
 (p↔q)↔((p→q)⋅(q→p))
 OR
 (p↔q)↔((p⋅q)V(p⋅q))

What does Exportation (Exp) look like?
((p⋅q)→r)↔(p→(q→r))

What does Tautology (Taut) look like?

What does Double Negation (DN) look like?
p↔p

What does Distribution (Dist) look like?
 (pV(q⋅r))↔((pVq)⋅(pVr))
 (p⋅(qVr))↔((p⋅q)V(p⋅r))