Logic

• Logic


  Study of correct and incorrect reasoning methods and principles
• Proposition


  Declarative statement that is either true or false
• Statement


  Asserted proposition, independent of the sentence used
• Argument


  A proposition used to support another
• Conclusion


  Proposition supported by other propositions in an argument
• Premise


  Propositions providing grounds for the conclusion in an argument
• Inference


  Process of affirming one proposition based on others
• Premise indicator


  Word or phrase signaling premises in an argument (e.g., "since", "because")
• Conclusion indicator


  Word or phrase indicating the conclusion in an argument (e.g., "therefore", "thus")
• Validity


  Deductive argument where true premises ensure a true conclusion
• Soundness


  Argument with both valid reasoning and true premises
• Fallacy


  Mistake in reasoning or argument error
• Syllogism


  Deductive argument with two premises and a conclusion
• Truth table


  Table determining truth values of propositions or arguments based on component truths
• Negation (¬)


  Logical NOT operator, reversing truth value
• Conditional (P → Q)


  Assertion that if P is true, then Q is true
• Antecedent (P)


  First proposition in a conditional statement
• Consequent (Q)


  Second proposition in a conditional statement
• Inverse


  Conditional with negated antecedent and consequent
• Converse


  Conditional with antecedent and consequent switched
• Contrapositive


  Conditional with both antecedent and consequent negated and switched
• Conjunction (∧)


  Logical AND operator, true if both propositions true
• Disjunction (∨)


  Logical OR operator, true if at least one proposition true
• Exclusive or (⊕)


  Logical XOR operator, true if only one proposition true
• Biconditional (↔)


  Logical 'IFF'/'If and only if' operator, true if both propositions true or false
• Modus Ponens


  If P implies Q, and P is true, then Q is true
• Modus Tollens


  If P implies Q, and Q is false, then P is false
• Hypothetical/Law of syllogism


  A --> B

  B --> C

  Therefore A--> C
• Deductive Logic


  When conclusion is garunteed to be true - premises are true
• Inductive logic

  When concslusion is likely to be true - premises must be true
• Conjecture


  Making an educated guess
• Counter-example


  A statement revealeaving a false conjecture
• Conjuction (^) 


  'AND' operator, only if both A and B are true
• Inclusive Disjuction (v)


  'OR' operator, only true if at least one of A and B are true
• Invalid Logic

  1. Converse Error
  2. Inverse Error
• Converse Error 


  A --> B

  B (T)

  Therefore A (T)
• Inverse Error


  A --> B

  ¬ A (F)

  Therefore ¬ B (F)
• Negation (¬)


  Logical 'NOT' operator, reversing truth value.
• Conditional (P -> Q)


  A proposition that one value implies another
• Straw man argument

  Type of fallacious reasoning, where oppoenents argument is misrepresented of oversimplified