Discrete Structures Homework #3

Due: Thursday, Sept. 19, 2002

Section 1.3 Exercises (pp. 41-45): 4, 7, 16

4. For each wff, find an interpretation in which it is true and one in which it is false.

(a is starred so its answer is given)

b.

c.

d.

e.

7. Using the predicate symbols shown and appropriate quantifiers, write each English language statement as a predicate wff. (The domain is the whole world.)

B(x) is "x is a ball."

R(x) is "x is round."

S(x) is "x is a soccer ball."

a. All balls are round.

b. Not all balls are soccer balls.

c. All soccer balls are round.

d. Some balls are not round.

e. Some balls are round but soccer balls are not.

f. Every round ball is a soccer ball.

g. Only soccer balls are round balls.

h. If soccer balls are round, then all balls are round.

16. Write the negation of each of the following.

a. Only students eat pizza.

b. Every student eats pizza.

c. Some students eat only pizza.