Answer to Question #308312 in Discrete Mathematics for ToBI

Question

[￢p ∧(p ∨ q)]→q

Answer 1

Solution

To prove

$[￢p ∧(p ∨ q)]→q$

$¬[¬p ∧ (p ∨ q)] ∨ q$

$(¬¬p ∨ ¬(p ∨ q)) ∨ q$

$p ∨ (¬p ∧ ¬q)) ∨ q$

$((p ∨ ¬p) ∧ (p ∨ ¬q)) ∨ q$

$(T ∧ (p ∨ ¬q)) ∨ q$

$(p ∨ ¬q) ∨ q$

$p ∨ (¬q ∨ q)$

$p ∨ T$

$T$