tautologies

tautologies - A List of Tautologies 1. 2. 3. 4. 5. 6. P P...

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A List of Tautologies 1. P ∨ ¬ P 2. ¬ ( P ∧ ¬ P ) 3. P P 4. a) P ( P P ) idempotent laws b) P ( P P ) 5. ¬¬ P P double negation 6. a) ( P Q ) ( Q P ) commutative laws b) ( P Q ) ( Q P ) c) ( P Q ) ( Q P ) 7. a) ( P ( Q R )) (( P Q ) R ) associative laws b) ( P ( Q R )) (( P Q ) R ) 8. a) ( P ( Q R )) (( P Q ) ( P R )) distributive laws b) ( P ( Q R )) (( P Q ) ( P R )) 9. a) ( P ∨ C ) P identity laws b) ( P ∧ C ) ↔ C c) ( P ∨ T ) ↔ T d) ( P ∧ T ) P 10. a) ¬ ( P Q ) ( ¬ P ∨ ¬ Q ) DeMorgan’s laws b) ¬ ( P Q ) ( ¬ P ∧ ¬ Q ) 11. a) ( P Q ) (( P Q ) ( Q P )) equivalence b) ( P Q ) (( P Q ) ( ¬ P ∧ ¬ Q )) c) ( P Q ) ( ¬ P ↔ ¬ Q ) 12. a) ( P Q ) ( ¬ P Q ) implication b) ¬ ( P Q ) ( P ∧ ¬ Q ) 13. ( P Q ) ( ¬ Q → ¬ P ) contrapositive 14. ( P Q ) (( P ∧ ¬ Q ) → C ) reductio ad absurdum 15. a) (( P R ) ( Q R )) (( P Q ) R ) b) (( P Q ) ( P R )) ( P ( Q R )) c) (( P Q ) ( P R )) ( P ( Q R )) 16. (( P Q ) R ) ( P ( Q R )) exportation law 17. P ( P Q ) addition 18.
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This note was uploaded on 03/29/2008 for the course MATH 220 taught by Professor Any during the Spring '08 term at Texas A&M.

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