Q: Which of the following statements about completeness and consistency in logical systems are correct?
(A) A formal logical system is complete if every logically valid sentence in its language is derivable in the system;
(B) A logical system is consistent if it does not prove both a sentence and its negation;
(C) Gödel’s incompleteness theorem, in one form, shows that sufficiently strong formal systems of arithmetic cannot be both complete and consistent;
(D) In simple propositional logic, standard proof systems are both complete and consistent;
(E) UGC NET Paper 1 typically expects only a basic idea of consistency and validity, not technical details of Gödel’s proofs;
(F) An inconsistent system can still be safely used for any logical reasoning because contradictions have no serious consequences;
Choose the correct answer from the options given below:
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