p → ¬q
p ∨ ¬q
q → p
p ∧ ¬q
¬p ∨ (p ∧ ¬q)
p | q | ¬p | ¬q | p ∧ ¬q | ¬p ∨ (p ∧ ¬q) | p → ¬q
T | T | F | F | F | F | F
T | F | F | T | T | T | T
F | T | T | F | F | T | T
F | F | T | T | F | T | T
The truth table shows that ¬p ∨ (p ∧ ¬q) is equivalent to p → ¬q.