Question 4
Let $K$ be a set of $n$ elements, where $n\ge5$. Consider any $n+1$ distinct three-element subsets of $K$.
a) Prove that one of these subsets, $A$, has the property that each element of $A$ also belongs to another subset in the family.
b) For $n=5$, prove that two of the six subsets have exactly one common element.
c) For $n=9$, prove that two of the ten subsets have exactly one common element.
a) Prove that one of these subsets, $A$, has the property that each element of $A$ also belongs to another subset in the family.
b) For $n=5$, prove that two of the six subsets have exactly one common element.
c) For $n=9$, prove that two of the ten subsets have exactly one common element.