PROOF

• This refers to a sequence of statements that end with conclusions.

  Argument
• This refers to conclusions that logically follow from the truth of the hypothesis

  Valid Argument / Proof
• This refers to an invalid argument.

  Fallacy
• These are established arguments used in proving more complex arguments.

  Rules of Interference
• Conjecture: statement proposed to be true
• Axiom: statement assumed to be true (a.k.a. Postulates, Laws)
• Theorem: statement shown to be true (a.k.a. facts, results)
• Corollary: theorems that follow directly from other theorems
• Lemma: a small theorem that is proven in a proof to help derive the next result.
• RECALL: The image is the same as (p → q) ∧ p → q, where (p → q) ∧ p are the premises and q is the conclusion.

  Type in skip: skip

  
• Modus Ponens: "method of affirming" or affirming the antecedent

  
• Modus Tollens: "mode that denies by denying" or denying the consequent

  
• Hypothetical Syllogism / Transitivity

  
• Disjunctive Syllogism: if there are only two possibilities, and one of them is ruled out, then the other must take place.

  
• Addition: disjunction introduction

  
• Simplification

  
• Conjunction

  
• Resolution

  
• Constructive Dilemma

  
• Destructive Dilemma

  
• This is a step in proving where we assume the truth of the premise of the statement to be proven.

  Conditional Proof / Direct Proof

  • Given an argument whose conclusion is a conditional statement, its proof is constructed by assuming the antecedent of its conclusion as the truth of the premise and then deducing the consequent of its conclusion.
• Universal Instantiation

  
• Universal Generalization

  
• Existential Instantiation

  
• Existential Generalization

  
• This happens when the hypothesis of the implication is always false, or in other words, when the proposition p (in if p, then q) is false.

  Vacuous Proof