DATA:¬ ≡ NOT ≡ ̅ OR ≡ ∨ ≡ +AND ≡ ∧ ≡ .Formula:a → b ≡ a̅ + bCalculation:S1 : (¬P ∧ (p ∨ q)) → q S1 ≡ (p̅.(p + q) → qS1 ≡ (p̅.p + p̅.q) → qS1 ≡ (p̅.q) → qS1 ≡ \(\overline{\overline p.q} + q\)S1 ≡ p + q̅ + q ≡ p + 1 ≡ 1S1 is a tautologyS2 ≡ q → (¬p ∧ (p ∨ q))S2 ≡ q → (p̅.(p + q))S2 ≡ q̅ + (p̅.p + p̅.q)) S2 ≡ q̅ + p̅.q ≡ p̅ + q̅ S2 is not a tautology.Therefore option 4 is correct "> DATA:¬ ≡ NOT ≡ ̅ OR ≡ ∨ ≡ +AND ≡ ∧ ≡ .Formula:a → b ≡ a̅ + bCalculation:S1 : (¬P ∧ (p ∨ q)) → q S1 ≡ (p̅.(p + q) → qS1 ≡ (p̅.p + p̅.q) → qS1 ≡ (p̅.q) → qS1 ≡ \(\overline{\overline p.q} + q\)S1 ≡ p + q̅ + q ≡ p + 1 ≡ 1S1 is a tautologyS2 ≡ q → (¬p ∧ (p ∨ q))S2 ≡ q → (p̅.(p + q))S2 ≡ q̅ + (p̅.p + p̅.q)) S2 ≡ q̅ + p̅.q ≡ p̅ + q̅ S2 is not a tautology.Therefore option 4 is correct ">
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Let p and q be two propositions. Consider the following two formulae in propositional logic.S1 : (¬p ∧ (p ∨ q)) → qS2 : q → (¬p ∧ (p ∨ q))Which one of the following choices is correct?

Logical and Verbal Reasoning Logic in Logical and Verbal Reasoning . 3 years ago

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DATA:¬ ≡ NOT ≡ ̅ OR ≡ ∨ ≡ +AND ≡ ∧ ≡ .Formula:a → b ≡ a̅ + bCalculation:S1 : (¬P ∧ (p ∨ q)) → q S1 ≡ (p̅.(p + q) → qS1 ≡ (p̅.p + p̅.q) → qS1 ≡ (p̅.q) → qS1 ≡ \(\overline{\overline p.q} + q\)S1 ≡ p + q̅ + q ≡ p + 1 ≡ 1S1 is a tautologyS2 ≡ q → (¬p ∧ (p ∨ q))S2 ≡ q → (p̅.(p + q))S2 ≡ q̅ + (p̅.p + p̅.q)) S2 ≡ q̅ + p̅.q ≡ p̅ + q̅ S2 is not a tautology.Therefore option 4 is correct
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Posted on 11 Aug 2021, this text provides information on Logical and Verbal Reasoning related to Logic in Logical and Verbal Reasoning. Please note that while accuracy is prioritized, the data presented might not be entirely correct or up-to-date. This information is offered for general knowledge and informational purposes only, and should not be considered as a substitute for professional advice.

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