Question 18 thank you Certainly! Below is a transcription of the text suitable for an educational website:---### Set Theory and Proofs1. If \( A, B, \) and \( C \) are sets, then \( A - B = \{ x : x \in A \text{ and } x \notin B \} \).2. \( A \cap (B \cup C) = (A \cap B) \cup (A \cap C) \).3. \( A \cup (B \cap C) = (A \cup B) \cap (A \cup C) \).4. \( A \cap (B - C) = (A \cap B) - (A \cap C) \).5. If \( p \) and \( q \) are positive integers, then \( \{pn : n \in \mathbb{N} \} \cap \{qn : n \in \mathbb{N} \} \neq \emptyset \).6. Suppose \( A, B, \) and \( C \) are sets. Prove that if \( A \subseteq B \), then \( A - C \subseteq B - C \).7. Suppose \( A, B, \) and \( C \) are sets. If \( B \subseteq C \), then \( A \times B \subseteq A \times C \).8. If \( A, B, \) and \( C \) are sets, then \( A \cup (B \cap C) = (A \cup B) \cap (A \cup C) \).9. If \( A, B, \) and \( C \) are sets, then \( A \cap (B \cup C) = (A \cap B) \cup (A \cap C) \).10. If \( A \) and \( B \) are sets in a universal set \( U \), then \( A \cap B = \overline{A \cup B} \).11. If \( A \) and \( B \) are sets in a universal set \( U \), then \( A \cup B = \overline{A \cap B} \).12. If \( A, B, \) and \( C \) are sets, then \( A - (B \cap C) = (A -

Name: Question 18 thank you Certainly! Below is a transcription of the text
Uploaded: 2024-03-20T07:07:12.000Z
Channel: Bartleby
Description: Question 18 thank you Certainly! Below is a transcription of the text suitable for an educational website:---### Set Theory and Proofs1. If \( A, B, \) and \( C \) are sets, then \( A - B = \{ x : x \in A \text{ and } x \notin B \} \).2. \( A \cap (B