Week 8

Question 1

Someone loves every problem set
• This sentence is true if
• A: for each problem set there is one student who loves it
• B: there is one student who loves every problem set
• C:both A and B
• D: none of the above

Answer 1

C

Question 2

Everyone in this room speaks two languages
• A:This sentence is ambiguous but only one of its reading is true for this room
• B:This sentences is ambiguous and all readings are true for this room
• C: this sentence is not ambiguous and it’s false
• D: this sentence is not ambiguous and it’s true

Answer 2

A
-Everyone in the room either speaks two different languages, or everyone in the room speaks only English and one other specific language (false for this room)

Question 3

How do we know they are determiners?

Answer 3

• they are in complementary distribution with other determiners
• things are in complementary distribution if they cannot occur at the same time in the same environment
  ex: you can’t say “some the student”
• exception: “all the men”

Question 4

Does “every elephant” in “every elephant is an avid hang glider?” denote a set of all elephants?

Answer 4

Yes

Question 5

no Canadian is an avid hang glider
• What does “no Canadian” denote?
• A: an empty set
• B: a set that might contains some individuals but none of them is a Canadian
• C: it’s not a set of individuals at all

Answer 5

B
-the set isn’t empty but it just doesn’t contain Canadians
if this is a set, what set exactly?

Question 6

the Law of Contradiction:

Answer 6

p and the negation of p can’t be simultaneously true

Question 7

-I am hungry. I am not hungry.
-Bruno is inside and Bruno is outside
These are examples of what?

Answer 7

the Law of Contradiction

Question 8

The Law of excluded middle:

Answer 8

either p or the negation of p is true

Question 9

Bruno is older than 19 years or younger than 19 years.

Example of what?

Answer 9

The Law of excluded middle

Question 10

Why do some quantifiers fail the law of contradiction and the law of excluded middle?

Answer 10

• we said that all determiners take a set denoted by a property and do something with it
• QPs are similar but different in that they take two sets denoted by two distinct properties and do something with them

Question 11

All Ontarians eat junkfood. ALL is doing what?

Answer 11

• ALL makes the first set into a subset of the second set

- any individual for which it is true that is Ontarian must also be true that it is a junk food-eater

Question 12

Some Ontarians eat junkfood. What is SOME doing?

Answer 12

• SOME means that the intersection of the first set and the second set is not empty
• the intersection of being Ontarian and being junk food-eater is not empty

Question 13

no Ontarians eat junkfood. What is NO doing?



Answer 13

NO means that the intersection of the first set and the second set is empty

Question 14

Three elephants are avid hang gliders
• what is the meaning of “three”?
• A: the set containing Fred, Bruno and Mary
• B: three means that there are exactly three elephants
• C: three means that the intersection of the set of elephants and the set of avid hang gliders has (exactly) three members

Answer 14

C

Question 15

• Does the order of the sets matter?
• A: yes, it does and I can think of an example
• B: no, it doesn’t
• C: I’m sure it does but I can’t think of an example

Answer 15

A
-Ex: All Ontarians are junk food-eaters
All junk food- eaters are Ontarians

Question 16

All Ontarians eat junk food
• If the order matters and Ontarians must be a subset of junk-food-eaters, can Americans be junk-food-eaters as well?
• A: yes, they can
• B: no, they can’t
• C: there are no Americans

Answer 16

A

Question 17

Quantifier meaning
ALL: 
SOME: 
NO: 
THREE:

Answer 17

ALL: set #1 is a subset of set #2
SOME: the intersection of set #1 and #2 is not empty
NO: the intersection of set #1 and #2 is empty
THREE: the cardinality of the intersection of set #1 and #2 is 3

Question 18

how do we know the order?

Answer 18

compositionality, semantic types

Question 19

Whats the difference between the law of contradiction and the law of excluded middle?

Answer 19

law of contradiction: can’t both be false

law of excluded middle: both can be false