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