[SOLVED] Stuck in Proof of Laws of Syllogism and Absorption in Propositional Logic!

Hello everyone, great this forum exists, I was just getting so hopeless...

Well I am badly stuck with the following problem, both problems are from Rosen section 1.2, I can't continue any further and am only still in section 1.2.

Please help(Later I'll also post my steps towards solution, I would like to know what went wrong.)

1) Prove that following statement is a tautology

(A -> B) /\ (B -> C) -> (A -> C)

Prove without using Truth Tables.

2) A \/ (A /\ B) = A

Please help, I am badly stuck, specially had given a lot of time to the first one.

Where are the references in the proof from?

Thanx Angel White! Thanx a lot! But where are the references from! I mean Table references and page references! Is it from Rosen itself.?

Some things wrong(As you said)

angel.white Thanx again for the clarification:

Unfortunately I am using Rosen 4th Edition,

anyways that version difference does not much matters if I understand it :

But I am having some doubts:

My derivation would go like this

(A -> B) */\ (B -> C) -> (A -> C)*

~[(~A V B) /\ (~B V C)] V (A -> C)

[~(~A V B) V ~(~B V C)] V (A -> C)

[(A /\ ~B) V (B /\ ~C)] V (A -> C)

Here on I get AND in the statement and thus on distributing it further it gets very complicated leading me no where.

Where am I wrong here?

Also I don't have that chain rule in any table, could you please mention it here.

About absorption law Table 6 mention in my version of my book something else, and no where it does mentions any absorption law in fact full question is following:

Prove:

a) [p V (p /\ q)] <=> p

b) [p /\ (p V q)] <=> p

Thus I have to prov both of them, I can;t use one for the other until I first prove the first one.

Thanx a lot man for the help....