Let F be a family of subsets of an n element set X

Question

The property that any two members of F meet

Answer 1

 

When two sets have elements in common, the set of these common elements is the intersection of the subsets.

Example:

If X is the set of all integers then we can define some subsets, F₁, F₂, F₃,... such that F={F₁ F₂ F₃ ...}.

Let F₁ be the set of multiples of 2 and F₂ be the set of multiples of 5.

10, 20, 30, 40, ... appear in F₁ and F₂ so we could define F₃={10 20 30 40 ...} and F₃=F₁∩F₂, because F₃ contains those elements common to F₁ and F₂. F₃ is also a subset of F, because F₁ and F₂ are subsets of F. F₁ and F₂ “meet” or intersect to produce F₃.

I hope this helps.