RECENT ASSIGNMENT

BIMLO 1 f
Describe all your steps carefully. It is the process that counts - even a correct solution without the described proof gets zero credit. Please write intelligibly.
Name: Date:
1. Is the following formula satisfiable?
(¬A ? (B ? C)) ?¬(C ? (A ? B))
2. For every pair of the following formulas, decide whether one follows from the other, or the other way round.
(A ? B) ? C
(A ? C) ? (B ? C)
(A ? C) ? (B ? C)
3. Find a formula using just the connectives ¬,? which is equivalent to the following formula.
(A ?¬B) ?¬(C ?¬(A ? B))
4. Find the disjunctive normal form of the formula (A ? (D ?¬E)) ? (C ?¬(A ? B)). Using this normal form, decide whether the formula is a consequence of (¬(E ? D)) ? A.
5. Is there a propositional formula ? using the variables A,B,C such that both ? ? (A?¬B ?C) and ? ?¬(A ? B) are tautologies?