Math 211

First Hour Exam

Name __________________________

Friday, September 26

95 points (will be normalized to 100)

1. (15 pts.) Let p be the statement “I study hard” and q the statement “I pass the test. Translate the following into symbolic form:

a) I study hard and I pass the test.

b) If I study hard then I pass the test

c) I pass the test only if I study hard.

2. (15 pts.) Given the statement “If it rains then I stay inside.” What is the

Sufficient condition?

Necessary condition?

Converse?

Contrapositive?

3. (10 pts.) Simplify the following expressions by moving the negation sign inside so that it appears only directly before the predicate expression(s).

4. (10 pts.) Construct a truth table for the expression . Please show your work.

5. (5 pts.) Let G(x) mean “x is a ground-feeding bird” and B(x) mean “x is brightly colored.”. Using quantifiers, translate the statement “No ground feeding bird is brightly colored.”

6. (10 pts.) Give a proof of the following, giving reasons for each step.

7. (15 pts.) Suppose that set A = {a, b, c}, and that B = {c, d}. What is the result of

8. (10 pts.) By showing each a subset of the other, prove that

9. (5 pts.) Say something about one of the following:

a) René Descartes

b) Georg Cantor

c) Charles Dodgson

d) Ada Augusta, Countess of Lovelace