Document not found! Please try again

Lecture 6: Valid Argument Forms

20 downloads 167 Views 25KB Size Report
Valid Argument Forms. Modus ponens ... therefore n is divisible by 10 or by 7 (by ...) ... or by 7. Conjunctive p ∧ q n is divisible by 2 and by 3 simplification I. ∴ p.
Valid Argument Forms p→q if n is divisible by 10, then n is divisible by 5 p n is divisible by 10 ∴q therefore n is divisible by 5 Modus tollels p→q if n is divisible by 10, then n is divisible by 5 ∼q n is NOT divisible by 5 ∴∼p therefore n is NOT divisible by 10 Disjunctive p n is divisible by 10 addition I ∴p∨q therefore n is divisible by 10 or by 7 (by ...) Disjunctive q n is divisible by 7 addition II ∴p∨q therefore n is divisible by 10 (by ...) or by 7 Conjunctive p∧q n is divisible by 2 and by 3 simplification I ∴p therefore n is divisible by 2 Conjunctive p∧q n is divisible by 2 and by 3 simplification II ∴ q therefore n is divisible by 3 Conjunctive p n is divisible by 9 addition q n is divisible by 12 ∴p∧q therefore n is divisible by 9 and by 12 Disjunctive p∨q n is divisible by 3 or by 7 syllogism I ∼q n is NOT divisible by 7 ∴p therefore n is divisible by 3 Disjunctive p∨q n is divisible by 3 or by 7 syllogism II ∼p n is NOT divisible by 3 ∴q therefore n is divisible by 7 Hypothetical p→q if n is divisible by 12, then n is divisible by 6 syllogism q→r if n is divisible by 6, then n is divisible by 3 ∴ p → r therefore if n is divisible by 12, then n is divisible by 3 Dilemma p∨q n is divisible by 8 or by 12 p→r if n is divisible by 8, then n is divisible by 4 q→r if n is divisible by 12, then n is divisible by 4 ∴r therefore n is divisible by 4 Rule of ∼ p → c if n is NOT divisible by 10, we obtain a contradiction contradiction ∴p therefore n is divisible by 10 Modus ponens