Prove the following using natural deduction
1. Given (m • (p ? q)), ((p v n) • ¬n), Prove q
2 Given ((p v q) • ? q), (p? ¬r), (s ? r), Prove (?s v t)
3. Given ((m • p) • ? r), (n ? r), ((?n v t) ? s) Prove s
Prove whether the following are valid inferences using the tree method
1. Given (m v n), (p ? r), (r v ¬n), Prove (m v z)
2. Given [(p ? q) v ¬q], q • m Prove(m • p) v (¬q ?r)
3. Given ? (r • (s • t)) , (s • r) , t ?q Prove q v s
4. Given ? (r v (s v t)) , (s v r) , t ?q Prove r
5. Given ? (r v s), (?s ? r), (? r v m) Prove m
7. Given ? (r v ?r) Prove m • z