Exercise · ZW-INTERSECTION-OF-FAMILIES-010 · ★★★ Advanced
Which of these families has empty intersection, but every pair of its members has nonempty intersection?
Choose one option.
Show answer
- D. \(\{\{1,2\}, \{2,3\}, \{1,3\}\}\)
Explanation
Its total intersection is \(\varnothing\), since no element lies in all three sets, yet each pair shares one: \(\{2\}\), \(\{1\}\) and \(\{3\}\).
Review the concept: Intersection of families
The intersection of a nonempty family \(\mathcal{F}\) of sets is the set \(\bigcap \mathcal{F}\) of objects that belong to every member of the family.
\[\bigcap \mathcal{F} = \{x \mid \forall A \in \mathcal{F},\ x \in A\}\]
More practice problems: intersection of families
- ZW-INTERSECTION-OF-FAMILIES-001 What does x ∈ bigcap F mean?
- ZW-INTERSECTION-OF-FAMILIES-002 If F = \A, B\, what is bigcap F?
- ZW-INTERSECTION-OF-FAMILIES-003 Which statement is true for every nonempty family F?
- ZW-INTERSECTION-OF-FAMILIES-004 Given F = \\a,b\,\b,c\\, what is bigcap F?
- ZW-INTERSECTION-OF-FAMILIES-005 Let F = \\1,2,3,4\, \2,4,6\, \4,5,6\\. What is bigcap F?
- ZW-INTERSECTION-OF-FAMILIES-006 What distinguishes x ∈ bigcap F from x ∈ bigcup F?
- ZW-INTERSECTION-OF-FAMILIES-007 Let F = \\1,…,k\ : k ∈ \3,5,7\\. What is bigcap F?
- ZW-INTERSECTION-OF-FAMILIES-008 Let F be a nonempty family and G ⊆ F a nonempty subfamily. What relation holds between bigcap F and…