1. v ~ Q P 2. · (~ v ) R T K 3. ~ K 4. ( · ~ ) v P Q K 5. ~ L P 6. ( ~ ) L P Q 7. ( v ) ( v ) M P Q R 8. [ v ( ) ] · ( ~ v ) P Q R R S 9. ( · ) v ~ P Q R ~ [ ( v ~ ) · ~ ] 10. P R S 11. ( v ) ~ Q P R 12. [ · ( ~ v ) ] v R T K S 13. ~ ~ K P 14. ( · ~ ) v ( ) P Q K R 15. ( ~ ) · ~ L P R 16. [ ( ~ ) ] ~ L P Q S [ ( v ) ( v ) ] v ( · ~ ) 17. M P Q R S P [ v ( ) ] ~ ( ~ v ) 18. P Q R R S 19. ( ) v (~ v ) P· Q R S 20. ~ [ ( ~ ) ( ~ v ) ] P R S Q · 21. ~ Q P ·Q 22. ( ) v (~ v ) R T K 23. P 24. ( · ~ ) · P Q K 25. ( ~ ) L P Q Exercises 7B.3 I. ∼ 1. Let = and = ( · ) S Shane is hungry, C Carly is hungry: S C The conjunction and Carly are hungry” contains two simple statements: is hungry,” “Shane “Shane and is hungry.” However, the main operator is a negation (“It is not the case that”); therefore the “Carly tilde must be placed outside the parentheses that contain the conjunction. 2. Let = = and = M I am mistaken, T my test score was high, H I am happy about the result. (∼ · · ∼ · (T · M T) H or M H)
1. ~ Q v P 2. R · (~ T v K ) 3. ~ K 4. ( P · ~ Q ) v K 5. L ~ P 6. ( L ~ P ) Q 7. ( M v P ) ( Q v R ) 8. [ P v ( Q R ) ] · ( ~ R v S ) 9. ( P · Q ) v ~ R 10. ~ [ ( P v ~ R ) · ~ S ] 11. ( ~ Q v P ) R 12. [ R · ( ~ T v K ) ] v S 13. ~ K ~ P 14. ( P · ~ Q ) v ( K R ) 15. ( L ~ P ) · ~ R 16. [ ( L ~ P ) Q ] ~ S 17. [ ( M v P ) ( Q v R ) ] v ( S · ~ P ) 18. [ P v ( Q R ) ] ~ ( ~ R v S ) 19. ( P· Q ) v (~ R v S ) 20. ~ [ ( P ~ R ) ( ~ S v Q ) ] 21. ~ Q · P 22. ( R ·Q ) v (~ T v K ) 23. P 24. ( P · ~ Q ) · K 25. L ( ~ P Q ) Exercises 7B.3 I. 1. Let S = Shane is hungry, and C = Carly is hungry: ∼ ( S · C ) The conjunction “Shane and Carly are hungry” contains two simple statements: “Shane is hungry,” and “Carly is hungry.” However, the main operator is a negation (“It is not the case that”); therefore the tilde must be placed outside the parentheses that contain the conjunction. 2. Let M = I am mistaken, T = my test score was high, and H = I am happy about the result. (∼ M · T) · H or ∼ M · (T · H)