Extra Practice Proofs with DN, MP, MT, &In, &Out

A.

1. (P&~Q)>(~R>(~S>T))
2. ~Q>(P&~T)
3. ~Q&~R   /:. S

B.

1. (A&~B)&(C&~D)
2. A>E
3. (E&~B)>F
4. G>B
5. (~G&C)>H
6. (H&F)>I  /:. I

C.

1. ~(Q&~R)>(~P&S)
2. (~P&S)>~T
3. T&S
4. ~R>(Q>U)  /:. T&U