Erdős–Ko–Rado theorem

The Erdős–Ko–Rado theorem is a fundamental result in combinatorial set theory, particularly in the area concerning intersecting families of sets. It was first proved by Paul Erdős, Chao Ko, and Ronald Rado in 1961. ### Statement of the Theorem: For a finite set \( X \) with \( n \) elements, let \( k \) be a positive integer such that \( k \leq \frac{n}{2} \).