## Chapter 14: PREDICATE LOGIC - Practice, Part A -

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No. of Questions= 30

Each item in this exercise is a sentence for you to put into the notation of predicate logic. Use x and y for variables. The letters you should use to represent predicates, variables, and names are listed for each sentence.

To indicate negation, use a tilde (~).
To indicate "or," use a lower-case "v" (v).
To indicate "if-then," use a greater-than symbol (>).
To indicate "and," use an asterisk (*).
To indicate "if and only if," use an equals sign (=).
To indicate the universal quantifier, place the variable inside parentheses.
To indicate the existential quantifier, place the variable after an upper-case "E" inside parentheses.

This exercise has three levels of difficulty. In (a) questions 1-12, the sentences will not require more than one quantifier and two predicates. In (b) questions 13-20, there may be more than two predicates. In (c) questions 21-25, there may be more than one quantifier.

 1. Dizzie Dean was a pitcher.Px: x is a pitcher d: Dizzie Dean 2. Either Carol will win or Jim will win.Wx: x will win c: Carol j: Jim 3. If Carol wins, she will be happy.Wx: x will win Hx: x will be happy c: Carol 4. Madonna is a singer and an actress.Sx: x is a singer Ax: x is an actress m: Madonna 5. There are miracles.Mx: x is a miracle 6. Some football players are smart.Fx: x is a football player Sx: x is smart 7. All babies are cute.Bx: x is a babyCx: x is cute 8. Some colleges do not have entrance requirements.Cx: x is a college Rx: x has entrance requirements 9. Everyone likes to discuss the weather.Px: x is a person Wx: x likes to discuss the weather 10. Some rules of logic are hard to remember.Rx: x is a rule of logic Hx: x is hard to remember 11. Construction crews are noisy.Cx: x is a construction crew Nx: x is noisy 12. Some people are lonely and sad.Px: x is a person Lx: x is lonely Sx: x is sad 13. Some black cats are good luck.Bx: x is black Cx: x is a cat Gx: x is good luck 14. All green or yellow vegetables are nutritious.Gx: x is a green vegetable Yx: x is a yellow vegetable Nx: x is nutritious 15. All seniors who have fulfilled the requirements will graduate in May.Sx: x is a senior Fx: x has fulfilled the requirementsGx: x will graduate in May 16. Some courses are difficult or boring.Cx: x is a course Dx: x is difficult Bx: x is boring 17. No car is both powerful and fuel-efficient.Cx: x is a carPx: x is powerful Fx: x is fuel-efficient Hint: There are two possible ways to correctly symbolize this proposition, both of which will be accepted by LogicTutor's scoring mechanism. 18. No car is both powerful and fuel-efficient.Cx: x is a carPx: x is powerful Fx: x is fuel-efficient Note: For this problem, you should use a different symbolization than you used for the problem 17. 19. Only skydivers with much experience perform in thrill shows.Sx: x is a skydiver Ex: x has much experience Px: x performs in thrill shows Hint: There are two possible ways to correctly symbolize this proposition, both of which will be accepted by LogicTutor's scoring mechanism. 20. Only skydivers with much experience perform in thrill shows.Sx: x is a skydiver Ex: x has much experience Px: x performs in thrill shows Note: For this problem, you should use a different symbolization than you used for the problem 19. 21. Jan loves Harry and Harry loves Jan.Lxy: x loves yj: Jan h: Harry 22. Jan loves someone or someone loves her.Lxy: x loves yj: Jan 23. Everyone loves a winner.Px: x is a person Wx: x is a winner Lxy: x loves y Hint: There are two possible ways to correctly symbolize this proposition, both of which will be accepted by LogicTutor's scoring mechanism. 24. Everyone loves a winner.Px: x is a person Wx: x is a winner Lxy: x loves y Note: For this problem, you should use a different symbolization than you used for the problem 23. 25. No buildings in Iceland are air-conditioned.Bx: x is a building Lxy: x is located in yAx: x is air-conditionedi: Iceland Hint: There are two possible ways to correctly symbolize this proposition, both of which will be accepted by LogicTutor's scoring mechanism. 26. No buildings in Iceland are air-conditioned.Bx: x is a building Lxy: x is located in yAx: x is air-conditionedi: Iceland Note: For this problem, you should use a different symbolization than you used for the problem 25. 27. I bought a car and it's a lemon.Cx: x is a car Bxy: x bought yLx: x is a lemon i: I Hint: There are two possible ways to correctly symbolize this proposition, both of which will be accepted by LogicTutor's scoring mechanism. 28. I bought a car and it's a lemon.Cx: x is a car Bxy: x bought yLx: x is a lemon i: I Note: For this problem, you should use a different symbolization than you used for the problem 27. 29. Some cruise ships do not stop at any islands.Cx: x is a cruise ship Ix: x is an island Sxy: x stops at y Hint: There are two possible ways to correctly symbolize this proposition, both of which will be accepted by LogicTutor's scoring mechanism. 30. Some cruise ships do not stop at any islands.Cx: x is a cruise ship Ix: x is an island Sxy: x stops at y Note: For this problem, you should use a different symbolization than you used for the problem 29.