Exercise · ZW-SET-007 · ★★☆ Intermediate
Two sets are equal when...
Choose one option.
Show answer
- C. They have exactly the same elements
Explanation
Two sets are equal if and only if they have exactly the same elements (extensionality). Having the same number of elements is not enough ({1,2} and {3,4}), containing each other in one direction is not enough either, and neither order nor the way they are written matters: {1,2} = {2,1}.
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-006 If A = \1,2,3\, which statement is true?
- ZW-SET-008 Which statement is true?
- ZW-SET-009 If A = {∅}, then...