Logic

[Tellos Athenaios]

ye, i just did this with my dad and we came to the same conclusion, but you explain it better than he did :P so thanx!

so the contradiction would be that H → F and F → H can't be true at the same time while the conditions demand them to be?

No the problem is that rule (3) and rule (4) require logical equivalence of F and H and it is not possible to prove this in the general case (i.e. using only the conditions/propositions given for any F, E, or H).

But it is perfectly possible there exist two propositions F, and H such that F -> H && H -> F:

Consider many of the basic examples of boolean algebra:
F: !A || (B && A)
H: !A || B
H <-> F