Chapter 6 - Set Theory - Exercise Set 6.1 - Page 350: 9

a. \( x \notin A \cup B \) if, and only if, \( x \notin A \) and \( x \notin B \). b. \( x \notin A \cap B \) if, and only if, \( x \notin A \) or \( x \notin B \). c. \( x \notin A - B \) if, and only if, \( x \in B \) or \( x \notin A \).

We use the definitions to complete the sentences: a. \( x \notin A \cup B \) if, and only if, \( x \notin A \) and \( x \notin B \). b. \( x \notin A \cap B \) if, and only if, \( x \notin A \) or \( x \notin B \). c. \( x \notin A - B \) if, and only if, \( x \in B \) or \( x \notin A \).