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Determine whether each of the following proposed proof systems aresound. Justify your answers.(a) Axioms: All

formulas.Rules: None.

(b) Axioms: None.Rules: From nothing, infer any formula.

(c) Axioms: All formulas of the form (P → P).Rules: Hypothetical Syllogism.

(d) Axioms: All formulas of the form (P → Q ).Rules: Modus Ponens.

(e) Axioms: All formulas of the form (P → Q ).Rules: Hypothetical Syllogism.

(f) Axioms: All tautologies.Rules: From any P that is not a tautology, infer any formula.

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