GATE CSE 1991 | Question: 03,xii

Question

If $F_1$, $F_2$ and $F_3$ are propositional formulae such that $F_1 \land F_2 \rightarrow F_3$ and $F_1 \land F_2 \rightarrow \sim  F_3$ are both tautologies, then which of the following is true:

• A. Both $F_1$ and $F_2$ are tautologies
• B. The conjunction $F_1 \land F_2$ is not satisfiable
• C. Neither is tautologous
• D. Neither is satisfiable
• E. None of the above

Comments

When taken individually F1 and F2 are tautologies, but when taken together it is a contingency.

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Answer by Deepak Sir . Very very important to understand the intricacies if this question.

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Find correct logic, correct answer for this question here:

https://gateoverflow.in/526/Gate-cse-1991-question-03-xii?show=374238#a374238

Answer 1

B.