p

p → q

therefore q 

¬ q

p → q

therefore ¬ p

p → q

q →  r

therefore p → r

p ∨ q

¬ p

therefore q

p

therefore p ∨ q 

p ∧ q

therefore p

p

q

therefore p ∧ q

p ∨ q

¬ p ∨ r

therefore q ∨ r

∀x P(x)

therefore P(c)

∃x P(x) 

therefore P(c) for an element c

P(c) for an arbitrary c

therefore ∀xP(x)

P(c) for some elemenet c

therefore ∃xP(x)

p ∧ q

¬ p ∨ r

*q ∨ r

*resolvent

p → q

q

p

incorrect reasoning b/c F when p ≡ F ∧ q

p → q

¬ p

 ¬ q

incorrect reasoning b/c F when p ≡ F AND q