$30.00

## Description

Problem 1. Textbook Section 1.1 Problem 12.

Problem 2. Textbook Section 1.1 Problem 14.

Problem 3. Write the following sets using set builder notations:

a) A = {1, 6, 11, 16, 21, . . . }.

_{1 } _{1 } _{1}

_{1 } _{1 } _{1 } _{1 } _{1}

^{b) } ^{B} ^{=} ^{{−} _{16} ^{,} ^{−} _{8 }^{,} ^{−} _{4 }^{,} ^{−} _{2 }^{,} _{2 }^{,} _{4 }^{,} _{8 }^{,} _{16} ^{}}^{.}

Problem 4. Is the emptyset ∅ an element of the following sets?

a) C = {{∅}}.

b) D = {{∅}, ∅}.

c) E = {{{∅}}, {∅}}.

Problem 5. Recall that for x ∈ R, we define the absolute value |x| of x by

^{(}_{x} _{if} _{x} _{≥} _{0}

^{|}^{x}^{|} ^{=}

−x if x ≤ 0 .

For a ∈ R we define the set A_{a} = {x ∈ R : 0 ≤ |x| ≤ −a^{2} + a + 2}.

1. Suppose that a = 1. What is A_{1}? (write it as an interval of R)

2. Suppose that a = −1. What is A_{−}_{1}? (write it as an interval of R)

3. Suppose that a = 2. What is A_{2}? (write it as an interval of R)

4. Is there a value of a for which A_{a } is empty?

Problem 6. Your solution to Section 2.2 Problem 8.

Page 1 Due on January 11