Question 110
The total number of languages used in KAUST is $n$. For each positive integer $k \leq n$, let $A_{k}$ be the set of all those people in KAUST who can speak at least $k$ languages; and let $B_{k}$ be the set of all people $P$ in KAUST with the property that, for any $k$ pairwise different languages (used in KAUST), $P$ can speak at least one of these $k$ languages. Prove that
a. If $2k \geq n+1$ then $A_{k} \subseteq B_{k}$;
b. If $2k \leq n+1$ then $A_{k} \supseteq B_{k}$.
a. If $2k \geq n+1$ then $A_{k} \subseteq B_{k}$;
b. If $2k \leq n+1$ then $A_{k} \supseteq B_{k}$.