Extra Problems Using RAA and ->I

1. B |- A -> A&B
2. A -> B&C |- A -> C
3. A -> (B -> C), ~C |- B -> ~A
4. B -> C |- (A ->B) -> (A -> C)
5. A -> (B -> C), A -> B |- A -> C
6. A -> B, A -> C |- A -> B&C
7. A&B -> C, B&C -> D |- A&B -> D
8. A v ~(B&C) |- B -> (C -> A)
9. A -> (B -> C), C -> D |- A -> (B -> D)
10. C |- A -> (B -> C)
11. A v B, A v ~B |- A
12. ~A -> B, ~(~A&B) |- A
13. A -> B&C, ~B |- ~A
14. A v (~B&C), B -> ~A |- ~B
15. A -> ~B, B v C, A v C |- C

If you have any trouble with these, you might want to look at the strategy sheet for some guidance.