1.6 Sets | 1.6 Sets | Unit 1: Proofs | Mathematics for Computer Science | Electrical Engineering and Computer Science

<Sets Operations: Video
1.6.1Sets Definitions: Video
1.6.2Sets Operations: Video
1.6.3Difference
>Binary Relations

Difference

For sets \(A\) and \(B\), which of the following are equivalent to \(A – B\)?

\(\{ x \mid (x \in A) \text{ AND } (x \in B) \} \)

\(\{ x \mid (x \in A) \text{ OR } (x \in B) \} \)

\(\{ x \mid (x \in A) \text{ AND } (x \notin B) \} \)

\(\{ x \mid (x \in A) \text{ AND } (x \in B) \} \)

\(\{ x \mid (x \in A) \text{ OR } (x \notin B) \} \)

\(\{ x \mid (x \notin A) \text{ OR } (x \in B) \} \)

In English, \(A-B\) is the set of elements in \(A\) and not in \(B\). Only \(\{ x \mid (x \in A) \text{ AND } (x \notin B) \} \) matches this description.