Assume that a proof system - is sound and complete with respect to a semantics E.Select all statements that are correct.a. {}# F, for any F. ({ } is the empty set)b. {P, P→Q, Q- -P} =RC.If S is consistent and S# F, then SEF.d. If S is inconsistent and F is a tautology, then S # F.

Option(b) is true because P implies Q , Q not implies P then is true to R.

Answered: Assume that a proof system F is sound…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Assume that a proof system F is sound and complete with respect to a semantics E. Select all statements that are correct. a. {}# F, for any F. ({ } is the empty set) O b. {P, P→Q, Q → ¬P} =R O c. If S is consistent and S F, then SEF. O d. If S is inconsistent and F is a tautology, then S # F.