Exercise · ZW-INTERSECTION-OF-FAMILIES-005 · ★★☆ Intermediate
Let \(\mathcal{F} = \{\{1,2,3,4\}, \{2,4,6\}, \{4,5,6\}\}\). What is \(\bigcap \mathcal{F}\)?
Choose one option.
Show answer
- A. \(\{4\}\)
Explanation
4 lies in all three sets. 2 fails in \(\{4,5,6\}\) and 6 fails in \(\{1,2,3,4\}\), so only \(\{4\}\) remains.
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-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…
- ZW-INTERSECTION-OF-FAMILIES-009 Let A_n = \x ∈ ℕ : x ≥ n\ for each n ∈ ℕ, with ℕ = \1,2,3,…\, and F = \A_n : n ∈ ℕ\. What is bigcap…
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