3. (50pts) Show that each of the following arguments is deductively

valid by providing a proof in SD (no shortcuts).

(a) (Y=(YM)), (Y&N), (N&M)

(b) ((PƆ (PQ)) :. (P>Q))

(c) (AB), (BƆ (C&D)), (C-D)-A

(d) (HƆ X). ((G&H) Ɔ (X VT))

(e) ((FV-H) (Z&K)), (ZƆ (→→W=P)),

P:

P. (FW)