HW 3: Sets

Introduction

In this homework you will gain practice working with sets.

Exercises

1. Problem 4.3 from the text.
2. Problem 4.4 from the text.
3. Problem 4.5 from the text.
4. Determine whether each of the following is true or false:

   1. 0 ∈ ∅
   2. ∅ ∈ {∅}
   3. ∅ ∈ {∅, {∅}}
   4. ∅ ⊆ {∅, {∅}}
   5. {∅} ∈ {∅, {0}}
   6. {∅} ⊆ {∅}
   7. {∅} ∈ {∅}

5. Let A and B be subsets of some universal set U. Show that A ⊆ B IFF B ⊆ A.
6. Define

   $\bigcup$_i=1…n A_i = A₁ ∪ A₂ ∪ … A_n and
   $\bigcap$_i=1…n A_i = A₁ ∩ A₂ ∩ … A_n

   Let A_i = {1, 2, 3, ..., i}. Find $\bigcup$_i=1…n A_i and $\bigcap$_i=1…n A_i.

Submit

When you are done, submit the .pdf file on Moodle.