# Brain Buster ( Comparison of ranking)

• Ali, Saad, and Hassan are all wise.
• Akram, Ali, and Hamza are all industrious.
• Akram, Hassan, and Hamza are all honest.
• Ali, Saad, and Hamza are all sportsmen.

Which of them are not wise, but is a sportsman?

1. Ali
2. Akram
3. Hassan
4. Hamza
• This is painfully simple. – generalcrispy Nov 13 '18 at 18:17

If we call the set of all sportsmen $$S = \{\textrm{Ali}, \textrm{Saad}, \textrm{Hamza}\}$$ and the set of all wise $$W = \{\textrm{Ali}, \textrm{Saad}, \textrm{Hassan}\}$$, we can deduce that $$S \land (\neg W) = \{\textrm{Hamza}\}$$. Therefore, Hamza is the only one who is a sportsman but is not wise.