### Assignment Instructions/ Description

Image transcription text1. [Set Operations] (4 points) Compute the sets using the following sets A, B, C and D.

A = {1, 2, 3, 4, 5,6} B= {1,3,5} C = (2, 4, 6} D = {1, 2,3}

(i) Cn (B - D)

(ii) (CnB) - D

(iii) B - Cc

(iv) (B - C)

2. [NP Denotations] (3 points) Give the denotations of the following NPs using set operations

on [happy], [hungry], [hippo], and [hamster].

(i) happy and hungry hippos

(ii) unhappy hippos

(iii) hungry hippos and happy hamsters

3. [Truth Conditions] (3 points) Give the truth conditions of the following sentences in terms

of [happy], [hungry], and [hippos].

(i) Every hippo is either happy or hungry.

(ii) More than two unhappy hippos aren't hungry.

(iii) Most hungry hippos are unhappy.

4. [Ambiguity] (4 points) The following expression (from the Rutgers family housing require-

ments) is ambiguous.

Married or single and living with children.

(i) Draw two trees to represent the two possible meanings. You don't need to break down

the tree for the VP 'living with children'

(ii) Give the denotations corresponding with each meaning in terms of set operations on

[married], [single], and [living with children].

5. [Relations] (2 points) Give the truth conditions for the following sentences in terms of [Ava],

[Hannah], [kitten], and the following relation [chase].

[chase] = {(x, y)|x chases y}

(i) Ava chases Hannah.

(ii) Ava chases every kitten.

6. [Monotonicity] (4 points) Determine whether the following environments are upward or

downward entailing. Give an example of two sentences for each to explain why.

(i) No

came to class.

(ii) Infinitely many students... Show moresemantics please help