DGD4:

(1) Arguments: 

(1a) Prove that the argument below is valid using (i) rules of inference and equivalences 
(see Examples 6 and 7 from Rosen, Section 1.6, for the format), (ii) truth trees. 

t -> ~(r \/ s)
u \/ t
u -> p
~p
--------------
Therefore ~r

(1b) determine whether the argument below is valid using (i)
truth tables, (ii) using truth trees; if it is invalid, give all counterexamples.

~(a <-> b)
a -> ~c
-----------
Therefore ~c -> b

(2) Proofs

(2a) Direct proof: Rosen 1.7 #6

(2b) Proof by contraposition: SE 3.11

(2c) Indirect proofs: by contraposition and by contradiction (emphasizing the
difference): Rosen 1.7 #18