Exercise · ZW-SET-OPERATIONS-008 · ★★★ Advanced
Let \(A\) and \(B\) be any sets. Which statement is always true?
Choose one option.
Show answer
- A. \(A\cap B\subseteq A\subseteq A\cup B\)
Explanation
Every element of \(A\cap B\) is in \(A\), and every element of \(A\) is in \(A\cup B\). The others fail, e.g. with \(A=\{1\}\) and \(B=\{2\}\).
Review the concept: Set operations
Set operations combine two sets \(A\) and \(B\), inside a universe \(U\), to form another one: union, intersection, difference and complement.
\[A\cup B,\quad A\cap B,\quad A\setminus B,\quad A^{c}=U\setminus A\]
More practice problems: set operations
- ZW-SET-OPERATIONS-001 Let A=\1,2,3,4,5\ and B=\4,5,6,7\. How many elements does A∪ B have?
- ZW-SET-OPERATIONS-002 With A=\1,2,3,4,5\ and B=\4,5,6,7\, what is A∩ B?
- ZW-SET-OPERATIONS-003 With A=\1,2,3,4,5\ and B=\4,5,6,7\, what is Asetminus B?
- ZW-SET-OPERATIONS-004 Let the universe be U=\1,2,3,4,5,6,7,8\ and A=\1,2,3,4,5\. What is the complement A^c?
- ZW-SET-OPERATIONS-005 With U=\1,2,3,4,5,6,7,8\, A=\1,2,3,4,5\ and B=\4,5,6,7\, what is (A∪ B)^c?
- ZW-SET-OPERATIONS-006 With U=\1,2,3,4,5,6,7,8\, A=\1,2,3,4,5\ and B=\4,5,6,7\, what is (A∩ B)^c?
- ZW-SET-OPERATIONS-007 Which expression equals the difference Asetminus B?
- ZW-SET-OPERATIONS-009 Let A be the even numbers from 1 to 20 and B the multiples of 3 from 1 to 20. What is A∩ B?