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Logic & Puzzles

A digital circuit design, represented as a CNF formula, contains a clause (A ∨ ¬A). If using a SAT solver, which consequence follows?

A)Solver finds unsat quickly
B)Solver performs unit propagation
C)Solver branches indefinitely
D)Clause simplifies to true immediately

💡 Explanation

Because the clause (A ∨ ¬A) is always true regardless of the value of A, the entire clause simplifies to 'true' via the tautology elimination mechanism; therefore the solver can remove this clause immediately, rather than getting stuck or finding unsat situations with contradictory unit propagation elsewhere.

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