We have two different logical formulas ($\psi$ and $\phi$). Is there a quick way to prove that if the formulas are equivalent (or not)? (if the formula $\psi$ is unsat also a formula $\phi$ is unsat (in SAT problem))
The equivalence of two different CNF logical formulas
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logic
1 Answers
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The simplest way would be to use a pair of truth tables, or if you want a quicker method two Karnaugh Maps.
When the first formula is unsatisfiable then it will contain all zeros on the truth table or in the Karnaugh Map. If the second formula has the same values in the Karnaugh Map or truth table then it will be unsatisfiable too.
If you are not familiar with Karnaugh Maps then I have a link here: https://www.facstaff.bucknell.edu/mastascu/eLessonsHTML/Logic/Logic3.html