Discussion
If F1, F2 and F3 are propositional formulae such that F1 ^ F2 → F3 and F1 ^ F2 → ˥F3 are both tautologies, then which of the following is TRUE?
Answer: B
Correct answer: The conjuction F1 ^ F2 is not satisfiable
If both implications are tautologies then whenever \( F_1 \land F_2 \) is true, F3 and its negation are both true - which is impossible. So \( F_1 \land F_2 \) can never be true, and it is unsatisfiable. Nothing follows about F1 or F2 individually; each may be satisfiable on its own.
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