Homework Solution: Given the following formula F: (P ∨ Q) → ((P ∨ Q ∨ ¬R) ∧ (R ∨ P ∨ Q))…

    Given the following formula F: (P ∨ Q) → ((P ∨ Q ∨ ¬R) ∧ (R ∨ P ∨ Q)) Using only the equivalence transformations in Propositional Logic, prove that the ¬F is a contradiction.

    Expert Answer

     
    Given formula F : (P ∨ Q

    Given the aftercited formula F: (P ∨ Q) → ((P ∨ Q ∨ ¬R) ∧ (R ∨ P ∨ Q))

    Using simply the equivalence transformations in Propositional Logic, test that the ¬F is a confliction.

    Expert Repartee

     

    Given formula F : (P ∨ Q) → ((P ∨ Q ∨ ¬R) ∧ (R ∨ P ∨ Q))

    equiv (P ∨ Q) → (P ∨ Q ∨ (¬R ∧ R)) (Associativity)

    equiv (P ∨ Q) → (P ∨ Q ∨ (false))       (AND production of two propositions)

    equiv (P ∨ Q) → (P ∨ Q)                   (Absorption)

    equiv penny (tautology)                         (An implication AB is is penny if twain penny or fallacious)

    So ¬F is a confliction.