Exercise · ZW-SET-006 · ★★☆ Intermediate
If \(A = \{1,2,3\}\), which statement is true?
Choose one option.
Show answer
- D. \(\{1\} \subseteq A\)
Explanation
\(\{1\} \subseteq A\) is true: the only element of \(\{1\}\) is 1, and 1 is in A. \(\{1,4\} \subseteq A\) is false because 4 is not in A, \(4 \in A\) is also false, and \(A \in 1\) makes no sense because 1 is not a set.
Review the concept: Set
A set is a well-defined collection of objects, called elements. Whether an object belongs to the set must be decidable without ambiguity.
\[x \in A \lor x \notin A\]
More practice problems: set
- ZW-SET-001 Which of the following best describes a set?
- ZW-SET-002 If x ∈ A, what does it mean?
- ZW-SET-003 If A = {1, 2, 3}, which statement is true?
- ZW-SET-004 Which symbol represents the empty set?
- ZW-SET-005 How many elements does A = {a, b} have?
- ZW-SET-007 Two sets are equal when...
- ZW-SET-008 Which statement is true?
- ZW-SET-009 If A = {∅}, then...