Question 43
Given an integer $k \ge 2$, exhibit an infinite set $\mathcal{A}$ of sets of positive integers satisfying the two conditions below:
(a) The intersection of the members of every $k$-element subset of $\mathcal{A}$ is a singleton set; and
(b) The intersection of the members of every $(k+1)$-element subset of $\mathcal{A}$ is empty.
(a) The intersection of the members of every $k$-element subset of $\mathcal{A}$ is a singleton set; and
(b) The intersection of the members of every $(k+1)$-element subset of $\mathcal{A}$ is empty.