# 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)

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