Originally Posted by

**natarajchakraborty** Ha I proved it!

I think I was going in right direction but giving up too soon...

I should have continued expansion.....

T stands for true/ tautology

(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)*

*<=> **[(A /\ ~B) V (B /\ ~C)] V (~A V C)*

*<=> [{B V **(A /\ ~B)} /\ {~C V **(A /\ ~B)}**]* V *(~A V C)*

*<=> [(B V A) /\ (B V ~B) /\ (~C V A) /\ (~C V ~B)] V **(~A V C)*

*<=> **[(B V A) /\ T /\ (~C V A) /\ (~C V ~B)] V **(~A V C)*

*<=> **[(B V A) /\ (~C V A) /\ (~C V ~B)] V **(~A V C)*

<=> [{~A V *(B V A)}** /\ {~A V **(~C VA)**} /\ {~A V **(~C V ~B)**}] V **[{C V **(B V A)}** /\ {C V **(~C V A)**} /\ {C V **(~C V ~B)**}]*

<=> [T /\ T /\ *{~A V **(~C V ~B)**}**] V [**{C V **(B V A)} /\ T /\ T**]*

<=> *[**~A V **(~C V ~B)**] V [**C V **(B V A)**]*

<=>* ~A V **(~C V ~B)** V **C V **(B V A)*

<=>* ~A V **~C V ~B** V **C V **B V A*

<=> (~A V A) V (~B V B) V (~ C V C)

<=> T V T V T

<=> T

QED