Matematisk Lingvistik VT98:03

Exercise class 1

Deadline

These exercises are supposed to be handed in on Tuesday April 7. Late exercises will receive one-point penalty per extra day. The exercises cover chapter 1 of the course book by Partee, Ter Meulen and Wall.

Notation

Because of the limitation of the range of characters in HTML I cannot display every character I need. I will use the following replacements in this exercise:

   A /\ B  the intersection of A and B
   A \/ B  the union of A and B
   P(A)    the power set of A
   A =< B  A is a subset of B
   A < B   A is a proper subset of B

Definitions

In these exercises we will use the definitions for 6 sets.

   A = { p , q , r , s }
   B = { q , r }
   C = { s , t }
   D = { { s } }
   E = Ø
   U = A \/ B \/ C \/ D     (universe)

Exercises

1. Determine which of the following statements are true:
   1. s is an element of A
   2. s is an element of B
   3. s is an element of D
   4. { s } is an element of C
   5. { s } is an element of D
   6. { s } =< C
   7. { s } =< D
   8. B < A
   9. C < A
   10. D < A

2. Compute the elements of
   1. A /\ C
   2. P(C) - D
   3. D' - B
   4. ( E \/ A )' /\ C

3. Use the laws presented in figure 1.7 (p18) of the course book to simplify the following set expressions:
   1. ( X /\ Y' ) \/ Y

   2. ( Y - X ) /\ ( X' \/ Z' )'

   X, Y and Z are arbitrary sets.

Each item in exercises 1 and 2 is worth 0.5 point. Each item in exercise 3 is worth 1.5 point.