Subcontests
(3)A subset of X with at least root 2n elements
Let X be an n-element set and let A1,…,Am be subsets of X such thati) ∣Ai∣=3 for each i=1,…,m.ii) ∣Ai∩Aj∣≤1 for any two distinct indices i,j.Show that there exists a subset of X with at least ⌊2n⌋ elements which does not contain any of the Ai’s.