HALF of a hypothetical proposition, WHENEVER the if-clause precedes the then-clause.A CONSEQUENT is the second half of a hypothetical proposition.Symbol:∧ = AND = .V = OR = +¬ = NOT ≡ ̅ 1 = TRUEFormula:A → B = ¬ A ∨ B = ¬ A + B¬ (A.B) = A̅ + B̅Calculation:Antecedent of S:(P ∧ Q)→ R ≡ ¬ (P.Q) + R ≡ P̅ + Q̅ + R Consequent of S:(P ∧ Q)→ (Q → R) ≡ ¬ (P.Q) + (¬ Q + R≡ P̅ + Q̅ + Q̅ + R ≡ P̅ + Q̅ + R Hence the antecedent of S is logically equivalent to the consequent of S.S = ((P ∧ Q)→ R)→ ((P ∧ Q)→ (Q → R))S = ¬ (¬ (P.Q) + R) + (¬ (P.Q) + (¬ Q + R))S = P.Q.¬R + ¬ P + ¬ Q. + (¬ Q + R)S = P.Q.R̅ + P̅ + Q̅ + Q̅ + RS = P.Q.R̅ + P̅ + Q̅ + R S = (P̅ + P)(P̅ + Q.R̅ ) + Q̅ + R // A + A̅B = A+ B S = P̅ + Q.R̅ + Q̅ + RS = P̅ + Q̅ + R̅ + RS = 1 = TRUE // A + A̅ = 1S is a tautology

"> HALF of a hypothetical proposition, WHENEVER the if-clause precedes the then-clause.A CONSEQUENT is the second half of a hypothetical proposition.Symbol:∧ = AND = .V = OR = +¬ = NOT ≡ ̅ 1 = TRUEFormula:A → B = ¬ A ∨ B = ¬ A + B¬ (A.B) = A̅ + B̅Calculation:Antecedent of S:(P ∧ Q)→ R ≡ ¬ (P.Q) + R ≡ P̅ + Q̅ + R Consequent of S:(P ∧ Q)→ (Q → R) ≡ ¬ (P.Q) + (¬ Q + R≡ P̅ + Q̅ + Q̅ + R ≡ P̅ + Q̅ + R Hence the antecedent of S is logically equivalent to the consequent of S.S = ((P ∧ Q)→ R)→ ((P ∧ Q)→ (Q → R))S = ¬ (¬ (P.Q) + R) + (¬ (P.Q) + (¬ Q + R))S = P.Q.¬R + ¬ P + ¬ Q. + (¬ Q + R)S = P.Q.R̅ + P̅ + Q̅ + Q̅ + RS = P.Q.R̅ + P̅ + Q̅ + R S = (P̅ + P)(P̅ + Q.R̅ ) + Q̅ + R // A + A̅B = A+ B S = P̅ + Q.R̅ + Q̅ + RS = P̅ + Q̅ + R̅ + RS = 1 = TRUE // A + A̅ = 1S is a tautology

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Choose the correct choice(s) regarding the following propositional logic assertion S:S : ((P ∧ Q)→ R)→ ((P ∧ Q)→ (Q → R))

Logical and Verbal Reasoning Logic in Logical and Verbal Reasoning . 5 months ago

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ConceptAn antecedent is the first HALF of a hypothetical proposition, WHENEVER the if-clause precedes the then-clause.A CONSEQUENT is the second half of a hypothetical proposition.Symbol:∧ = AND = .V = OR = +¬ = NOT ≡ ̅ 1 = TRUEFormula:A → B = ¬ A ∨ B = ¬ A + B¬ (A.B) = A̅ + B̅Calculation:Antecedent of S:(P ∧ Q)→ R ≡ ¬ (P.Q) + R ≡ P̅ + Q̅ + R Consequent of S:(P ∧ Q)→ (Q → R) ≡ ¬ (P.Q) + (¬ Q + R≡ P̅ + Q̅ + Q̅ + R ≡ P̅ + Q̅ + R Hence the antecedent of S is logically equivalent to the consequent of S.S = ((P ∧ Q)→ R)→ ((P ∧ Q)→ (Q → R))S = ¬ (¬ (P.Q) + R) + (¬ (P.Q) + (¬ Q + R))S = P.Q.¬R + ¬ P + ¬ Q. + (¬ Q + R)S = P.Q.R̅ + P̅ + Q̅ + Q̅ + RS = P.Q.R̅ + P̅ + Q̅ + R S = (P̅ + P)(P̅ + Q.R̅ ) + Q̅ + R // A + A̅B = A+ B S = P̅ + Q.R̅ + Q̅ + RS = P̅ + Q̅ + R̅ + RS = 1 = TRUE // A + A̅ = 1S is a tautology

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Posted on 02 Nov 2024, 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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