Question 144
Let $\mathcal{S}$ be a family of $n$ sets, each of size $k$, such that $A \Delta B \in \mathcal{S}$ whenever $A, B \in \mathcal{S}, A \neq B$.
a) Is it possible that $n = 2023$? If it is, find all possible values of $k$.
b) Is it possible that $n = 1023$? If it is, find all possible values of $k$.
Notation: $A \Delta B = (A \setminus B) \cup (B \setminus A)$.
a) Is it possible that $n = 2023$? If it is, find all possible values of $k$.
b) Is it possible that $n = 1023$? If it is, find all possible values of $k$.
Notation: $A \Delta B = (A \setminus B) \cup (B \setminus A)$.