1. 24.903
Language & Structure III: Semantics and Pragmatics
Spring 2003, 2-151, MW 1-2.30
April 9, 2003
Assignment 7, due in class on April 16
1. Consider the following structure:
(1) [[Mary jogs] [or [[Mary swims] [or [Mary dances]]]]].
What are the predicted truth conditions of (1) under the following circumstances (i) if all the or’s are inter-
preted as inclusive, and (ii) if all the or’s are interpreted as exclusive.
Situation ª
 Ë
 Ë
 Ë
 Ë
 Ë
 Ë
 Ë
 Ë
2. This exercise is about the entailment relations between sentences involving inclusive or, exclusive or, and
and. Consider the following six claims.
For any pair of sentences S½ and S¾ ,
a. ‘S½ or Ò Ð S¾ ’ entails ‘S½ or Ü Ð S¾ ’.
b. ‘S½ or Ü Ð S¾ ’ entails ‘S½ or Ò Ð S¾ ’.
c. ‘S½ or Ò Ð S¾ ’ entails ‘S½ and S¾ ’.
d. ‘S½ and S¾ ’ entails ‘S½ or Ò Ð S¾ ’.
e. ‘S½ or Ü Ð S¾ ’ entails ‘S½ and S¾ ’.
f. ‘S½ and S¾ ’ entails ‘S½ or Ü Ð S¾ ’.
Which of these claims are correct, and which are false? Justify your answers. Include concrete counterex-
amples to each of the claims that are false.
2. 3. Consider the following claims involving ª?
For any Ô Õ Ö ,
a. Is Ô ª Ô Ô ? (Idempotency)
b. Is Ô ª Õ Õ ª Ô? (Commutativity)
c. Is ´Ô ª Õ µ ª Ö Ô ª ´ ª µ? (Associativity)
Õ Ö
d. Is Ô ª ´Õ ª Öµ ´ ª µ ª ´ ª µ?
Ô Õ Ô Ö
e. Is Ô ´Õ ª Öµ ´
Ô µª´
Õ µ?
Ô Ö
f. Is Ô ´Õ ª Öµ ´
Ô µª´
Õ µ?
Ô Ö
g. Is Ô ª ´Õ Öµ ´ ª µ ´ ª µ?
Ô Õ Ô Ö
h. Is Ô ª ´Õ Öµ ´ ª µ ´ ª µ?
Ô Õ Ô Ö
Which of these claims are correct, and which are false? Justify your answers. Include concrete counterex-
amples to each of the claims that are false.
4. Consider the following logical expression: Ô½ ª Ô¾ ª ª ÔÒ .
a. Under what circumstances is this logical expression true?
b. Under what circumstances is this logical expression false?
(Assume Ò ¾.)
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