Premise 1: R∨T
Premise 2: ∼P↔(∼P→Q)
Prove: (R∨S)∨(T∧Q), using only R, DN, MP, MT, S, ADJ, MTP, ADD, BC, CB, CDJ, DM.
Here's what I got so far:
- Show (R∨S)∨(T∧Q)
R∨T______________________________________PR1
∼P↔(∼P→Q)______________________________PR2
∼P→(∼P→Q)______________________________3 BC
(∼P→Q)→∼P______________________________3 BC
- Show ~P→Q
~P_____________________________ASS CD
∼P→Q_________________________4 7 MP
Q______________________________7 8 MP
_______________________________9 CD
~P_______________________________________5 6 MP
Q________________________________________6 11 MP
Now, I'm not sure how to find the answer. I'm pretty sure that I have to either prove R or T by indirect derivation, but I can't seem to find a way to have a contradiction. Is there another way?