Set theory puzzles - chess players and mathematicians I'm looking at "Basic Set Theory" by A. Shen.  The very first 2 problems are: 1) can the oldest mathematician among chess players and the oldest chess player among mathematicians be 2 different people? and 2) can the best mathematician among chess players and the best chess player among mathematicians be 2 different people?  I think the answers are no, and yes, because a person can only have one age, but they can have separate aptitudes for chess playing and for math.  Is this correct?

(1) Think of it in terms of sets. Let $M$ be the set of mathematicians, $C$ the set of chess players. Both are asking for the oldest person in $C\cap M$.
(2) Absolutely fantastic reasoning, though perhaps less simply set-theoretically described.
