## Description

Problem 1. (25 points)

Suppose that A, B, and C are sets. Prove or disprove that (A − B) − C = (A − C) − B.

Problem 2. (25 points)

Determine whether the symmetric difference is associative; that is, if A, B, and C are sets, does it follow

that A ⊕ (B ⊕ C) = (A ⊕ B) ⊕ C?

a. Use a Venn diagram.

b. Use a membership table.

c. Use set identities.

Problem 3. (25 points)

Determine whether f is a function from Z to R if

a. f(n) = ±n

b. f(n) = ln

2

m

c. f(n) = √

n2 + 1

d. f(n) = √

n

e. f(n) = 1

n2 − 4

Problem 4. (25 points)

Consider the function f : Z → (N − {0}) where f(n) =

1 − 2n n ≤ 0

2n n > 0

a. Prove that f is a bijection by showing that it is both injective and surjective.

b. Find the inverse function f

−1

.

1

Aggie Honor Statement: On my honor as an Aggie, I have neither given nor received any unauthorized

aid on any portion of the academic work included in this assignment.

Checklist: Did you…

1. abide by the Aggie Honor Code?

2. solve all problems?

3. start a new page for each problem?

4. show your work clearly?

5. type your solution?

6. submit a PDF to eCampus?

2