Question & Answer: Use the laws of propositional logic to prove that the following compound propositions are logically equivalent. Indicate the law(s) used in…..

(30 pt. Part Il: Proving logical equivalence using laws of propositional logic 1. (20 pt, 5 pt. each) Use the laws of propositional logic to prove that the following compound propositions are logically equivalent. Indicate the law(s) used in each step of the proof (p-, q) v (p → r) and p → (q vr) vb. , p←→ q and (p ^ q) v (-p^-q) »-(avr) and (p ^-q) → r -Crv(qAGr→-p)))and-r^@v-q) (10 pt, 5 pt. each) Use the laws of propositional logic to prove that the following compound propositions are tautologies. Indicate the law(s) used in each step of the proof

Use the laws of propositional logic to prove that the following compound propositions are logically equivalent. Indicate the law(s) used in each step of the proof. a. (p rightarrow q) logicalor (p rightarrow r) and p rightarrow (q logicaland r) b. p doubleheadarrow q and (p logicaland q) logicalor (p logicaland q) c. p rightarrow (q logicalor r) and (p logicaland q) rightarrow r d. (r logicalor (q logicaland (r rightarrow p))) and r logicaland (p logicalor q) Use the laws of propositional logic to prove that the following compound propositions are tautologies. Indicate the law(s) used in each step of the proof. a. (p logicaland (p logicalor q)) rightarrow q b. (p logicalor q) logicaland (p logicalor r) rightarrow (q logicalor r)

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