3.1 Statements and Logical Connectives 105 6. a) The conditional is symbolized by → and is read “____________.” If–then b) The biconditional is symbolized by ↔ and is read “____________.” If and only if Practice the Skills/Problem Solving In Exercises 7–16, write the negation of the statement. 7. All flowers are perennials. Some flowers are not perennials. 8. No clouds are cumulus. Some clouds are cumulus. 9. Some turtles do not have claws. All turtles have claws. 10. All iPhones run on an IOS operating system. Some iPhones do not run on an IOS operating system. 11. No bicycles have three wheels. Some bicycles have three wheels. 12. All horses have manes. Some horses do not have manes. 13. Some pedestrians are in the crosswalk. No pedestrians are in the crosswalk. 14. Some teachers are not professors. All teachers are professors. 15. No mountain climbers are teachers. Some mountain climbers are teachers. 16. Some vitamins contain sugar. No vitamins contain sugar. In Exercises 17–26, indicate whether the statement is a simple statement or a compound statement. If it is a compound statement, indicate whether it is a negation, conjunction, disjunction, conditional, or biconditional by using both the word and its appropriate symbol (for example, “a negation,” ∼). 17. Cindy is a yoga instructor. Simple statement. 18. If you get up early, you will have time for breakfast. Compound; conditional, → 19. Time will go backward if and only if you travel faster than the speed of light. Compound; biconditional, ↔ 20. Miles Davis did not play rap music. Compound; negation, ∼ 21. Vin Diesel makes an appearance in Fast X and Guardians of the Galaxy Vol. 3. Compound; conjunction, ∧ 22. The book was neither a novel nor an autobiography. Compound; conjunction, ∧ 23. If Andres plays in the World Cup, then he will play for Spain. Compound; conditional, → 24. The Lightning will make the playoffs if and only if they win their last five games. Compound; biconditional, ↔ 25. It is false that Jeffery is a high school teacher and a grade school teacher. Compound; negation, ∼ 26. The hurricane did $400,000 worth of damage to DeSoto County. Simple statement In Exercises 27–32, write the statement in symbolic form. Let p q : A panther has a long tail. : A bobcat can purr. 27. A panther has a long tail and a bobcat can purr. ∧ p q 28. A panther does not have a long tail and a bobcat can purr. p q ∼ ∧ 29. A bobcat cannot purr or a panther does not have a long tail. q p ∼ ∨ ∼ 30. A bobcat cannot purr if and only if a panther does not have a long tail. q p ∼ ↔∼ 31. If a panther does not have a long tail, then a bobcat cannot purr. p q ∼ →∼ 32. A bobcat cannot purr, but a panther has a long tail. q p ∼ ∧ In Exercises 33–38, write the statement in symbolic form. Let p q : The eggs are organic. : The omelet contains cheese. 33. The eggs are organic and the omelet does not contain cheese. p q ∧ ∼ 34. If the eggs are not organic, then the omelet contains cheese. p q ∼ → 35. The omelet does not contain cheese if and only if the eggs are organic. q p ∼ ↔ 36. The eggs are not organic or the omelet does not contain cheese. p q ∼ ∨ ∼ 37. It is false that the eggs are organic or the omelet contains cheese. ∼ ∨ p q ( ) 38. It is false that if the omelet does not contain cheese then the eggs are organic. q p ( ) ∼ ∼ → Donyanedomam/ 123RF *See Instructor Answer Appendix
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