## Chapter 14: PREDICATE LOGIC

- Practice, Part A -Fill-In

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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 Dean2.Either Carol will win or Jim will win.

Wx: x will win

c: Carol

j: Jim3.If Carol wins, she will be happy.

Wx: x will win

Hx: x will be happy

c: Carol4.Madonna is a singer and an actress.

Sx: x is a singer

Ax: x is an actress

m: Madonna5.There are miracles.

Mx: x is a miracle6.Some football players are smart.

Fx: x is a football player

Sx: x is smart7.All babies are cute.

Bx: x is a baby

Cx: x is cute8.Some colleges do not have entrance requirements.

Cx: x is a college

Rx: x has entrance requirements9.Everyone likes to discuss the weather.

Px: x is a person

Wx: x likes to discuss the weather10.Some rules of logic are hard to remember.

Rx: x is a rule of logic

Hx: x is hard to remember11.Construction crews are noisy.

Cx: x is a construction crew

Nx: x is noisy12.Some people are lonely and sad.

Px: x is a person

Lx: x is lonely

Sx: x is sad13.Some black cats are good luck.

Bx: x is black

Cx: x is a cat

Gx: x is good luck14.All green or yellow vegetables are nutritious.

Gx: x is a green vegetable

Yx: x is a yellow vegetable

Nx: x is nutritious15.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 May16.Some courses are difficult or boring.

Cx: x is a course

Dx: x is difficult

Bx: x is boring17.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: Harry22.Jan loves someone or someone loves her.

Lxy: x loves y

j: Jan23.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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