Notes From CS Undergrad Courses FSU
This project is maintained by awa03
| p | q | r | p ∧ q | q ⊕ r | (p ∧ q)∨ r | (q ⊕ r) ∧ p | P |
|---|---|---|---|---|---|---|---|
| T | T | T | T | F | T | F | F |
| T | T | F | T | T | T | T | T |
| T | F | T | F | T | T | T | T |
| T | F | F | F | F | F | F | T |
| F | T | F | F | T | F | F | T |
| F | F | T | F | T | F | F | F |
| F | F | F | F | F | F | F | T |
LHS of P RHS of P
| LHS | RHS | LHS->RHS |
|---|---|---|
| T | T | T |
| T | F | F |
| F | T | T |
| F | F | T |
The premise is true ∧ the conclusion is false -- if then is false
P = ¬(LHS) ∨ (RHS) = [¬(p ∧ q) ∧ (¬ r)] ∨ [((q ∧ (¬ r)) ∨ (¬ q ∧ r)) ∨ p] = [(¬ p) ∨ (¬ q) ∧ (¬ r)] ∨ [(q ∧ (¬ r) ∧ p) ∨ (¬ q ∧ r) ∧ p] = [¬ p ∧ ¬ r] ∨ [¬ q ∧ ¬ r] ∨ [q ∧ ¬ r ∧ p] ∨ [¬ q ∧ r ∧ p]
This leads to the same result as the above table, similar to algebra f∨ f∨mal logic
Compound propositions P ∧ Q are described in terms of atomic propositions p, q, r, ... are logically equivalent. This is written as
$P ≡ Q (∨ P <==> Q)$
if P ∧ Q has identical truth values this means...