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 baby
Cx: 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 requirements
Gx: 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 car
Px: 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 car
Px: 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 y
j: Jan
h: Harry
22 Jan loves someone or someone loves her.
Lxy: x loves y
j: 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 y
Ax: x is air-conditioned
i: 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 y
Ax: x is air-conditioned
i: 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 y
Lx: 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 y
Lx: 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.




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