Mathematics 220 Homework #1 Solution

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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 Aa = {x R : 0 |x| a2 + a + 2}.

1. Suppose that a = 1. What is A1? (write it as an interval of R)

2. Suppose that a = 1. What is A1? (write it as an interval of R)

3. Suppose that a = 2. What is A2? (write it as an interval of R)

4. Is there a value of a for which Aa is empty?

Problem 6. Your solution to Section 2.2 Problem 8.

Page 1 Due on January 11