Exercise · ZW-RELATIVE-COMPLEMENT-008 · ★★☆ Intermediate
If \(A \setminus B = \varnothing\), what can be concluded?
Choose one option.
Show answer
- B. \(A \subseteq B\)
Explanation
No element of \(A\) lies outside \(B\), so \(A \subseteq B\). With \(A = \{1\}\) and \(B = \{1,2\}\) we get \(A \setminus B = \varnothing\), yet \(B \not\subseteq A\) and \(A \neq B\).
Review the concept: Relative complement
The relative complement of \(B\) in \(A\) is the set \(A \setminus B\) of elements of \(A\) that do not belong to \(B\).
\[A \setminus B = \{x \in A : x \notin B\}\]
More practice problems: relative complement
- ZW-RELATIVE-COMPLEMENT-001 What does x ∈ A setminus B mean?
- ZW-RELATIVE-COMPLEMENT-002 If A = \a,b,c\ and B = \b\, what is A setminus B?
- ZW-RELATIVE-COMPLEMENT-003 What is A setminus A?
- ZW-RELATIVE-COMPLEMENT-004 What relation does A setminus B satisfy with A?
- ZW-RELATIVE-COMPLEMENT-005 Let A = \1,…,10\ and B = \2,4,6,8,10,12\. What is A setminus B?
- ZW-RELATIVE-COMPLEMENT-006 Which statement is true for any sets A and B?
- ZW-RELATIVE-COMPLEMENT-007 How many elements does \2,4\ setminus A have, if A = \1,2,3,4\?
- ZW-RELATIVE-COMPLEMENT-009 Let A = \1,…,20\, B_1 = A setminus \x : x is even\ and B_2 = A setminus B_1. What is B_2?