Proof Tautology

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  • 7/25/2019 Proof Tautology

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    [(p q) (q r)] (p r) (Definition)

    [(p q) (q p) (q r) (r q)] [(p r) (r p)] ( )

    [(p q) (q p) (q r) (r q)] [(p r) (r p] (De Morgan)

    [(p q) q] [(p q) p]

    [(q r) r] [(q r) q]

    [(p r) (r p)] (Distributivity)

    [(p q) (q q)] [(p p) (q p)]

    [(q r) (r r)] [(q q) (r q)]

    [(p r) (r p] (Distributivity)

    [(p q) T] [T (q p)]

    [(q r) T] [T (r q)]

    [(p r) (r p)] (Negation)

    [(p q) (q p)] [(q r) (r q)] [(p r) (r p)] (Identity)

    [(p q) (q p)] (q r)

    [(p q) (q p)] (r q)

    [(p r) (r p)] (Distributivity)

    [(p q) (q r)] [(q p) (q r)]

    [(p q) (r q)] [(q p) (r q)]

    [(p r) (r p)] (Distributivity)

    [(p q) (q r)] [(q q) (p r)]

    [(q q) (p r)] [(q p) (r q)]

    [(p r) (r p)] (Associativity)

    [(p q) (q r)] [T (p r)]

    [T (p r)] [(q p) (r q)]

    [(p r) (r p)] (Negation)

    [(p q) (q r)] T

    T [(q p) (r q)]

    [(p r) (r p)] (Domination)

    [(p q) (q r)] [(q p) (r q)]

    [(p r) (r p)] (Identity)

    [(p q) (q r)] [(p r) (r p)]

    [(q p) (r q)] [(p r) (r p)]

    (Distributivity)

    [(p q) (q r)] (p r)

    [(p q) (q r)] (r p)

    [(q p) (r q)] (p r)

    [(q p) (r q)] (r p)

    (Distributivity)

    [(p p) q q r r] [(r r) p q q p]

    [(r r) q p q p] [(p p) q r q r]

    (Associativity)

    [T q q r r] [T p q q p]

    [T q p q p] [T q r q r]

    (Negation)

    (T T) (T T) (Domination)

    T T T T (Associativity)

    T (Identity)