MATH 350 Homework 01

1. What is the samlpe space for the following random experiments?
   1. Zip codes are collected at a gas station.
   2. The lifetime of a computer on the Chico State campus.
   3. 50 random people are selected and the number of "morning-people" are counted.
2. Suppose $S = \{1, 2, 3, 4, 5, 6\}$. Consider the sets $A = \{ 1, 2, 3 \}$ and $B = \{2, 4, 6 \}$.
   1. Write in your own words the definition of the intersection of two sets.
   2. What set is the intersection of the sets $A$ and $B$, $A \cap B$?
   3. Write in your own words the definition of the union of two sets.
   4. What set is the union of the sets $A$ and $B$, $A \cup B$?
   5. Write in your own words the definition of the complement of the set $A$, $A^c$.
   6. What set is the complement of $A^c$ relative to $S$?
   7. Provide a set that is a subset of $S$, but different from $A$ and $B$.
3. Suppose $S = \{ A, E, I, O, U \}$. Provide three sets which form a partition of $S$, e.g. are non-empty, mutually exclusive, and exhaustive of $S$.
4. Suppose $A = \{ a, b, c \}$. Provide a non-empty set which shares no items in common with $A$, name it $C$. What is the set defined by $A \cap C$? Identify the name of this set and write it out mathematically.
5. What must be true of events $A$ and $B$, if $A \cup B = B$, $A \cap B = A$, and $A \neq B$? Please write your answer using both symbols and words.
6. Suppose $A_1, A_2, \ldots, A_k$ are intervals of real numbers such that $A_i = \{x : 0 \leq x < 1 / i \}$ for $i = 1, 2, \ldots, k$. Using symbols and words, describe the sets
   1. $\cup_{i=1}^k A_i$
   2. $\cap_{i=1}^k A_i$