Question 139
Given a positive integer $n \ge 2$, let $B_1, B_2, \dots, B_n$ denote $n$ arbitrary subsets of set $X$, each of which contains exactly two elements. Find the minimum value of $|X|$ such that there exists a subset $Y$ of set $X$ satisfying:
(a) $|Y| = n$;
(b) $|Y \cap B_i| \le 1$ for $i = 1, 2, \dots, n$,
where $|A|$ denotes the number of elements of the finite set $A$.
(a) $|Y| = n$;
(b) $|Y \cap B_i| \le 1$ for $i = 1, 2, \dots, n$,
where $|A|$ denotes the number of elements of the finite set $A$.