Logic

  Law of  inferences  Here are the symbols of various logical operators as I use them on this website (there is no one, universal list of symbols, though certain norms are adhered to across the spectrum): ∧ = And ∨ = Or → = If…then ¬  = Not (negation) ≡   = Logical Equivalence Here are the most common inferences in symbolic logic: 1) Modus Ponens (MP) P → Q P  Therefore, Q 2) Modus Tollens (MT) P → Q ¬Q  Therefore, ¬P 3) Hypothetical Syllogism (HS) P → Q Q → R  Therefore, P → R 4) Disjunctive Syllogism (DS) P ∨ Q ¬P Therefore, Q 5) Simplification (SIMP) P ∧ Q   Therefore, P 6) Addition (ADD) P  Therefore, P ∨ Q 7) Double Negation (DN) P   Therefore, ¬¬P 8) Conjunction (CONJ) P Q  Therefore, P ∧ Q 9) Constructive Dilemma (CD) (P → Q) ∧ (R → S) P ∨ R  Therefore, Q ∨ S 10) Destructive Dilemma (DD) (P → Q) ∧ (R → S) ¬Q ∨ ¬S   Therefore, ¬P ∨ ¬R Finally, here are the 9 logical equivalences: 1) De Morgan’...