Every young woman should take courses in Logic and read Euclid’s Elements.  

The Elements (Ancient Greek: Στοιχεῖον Stoikheîon) is a mathematical treatise consisting of 13 books attributed to the ancient Greek mathematician Euclid in Alexandria, Ptolemaic Egypt c. 300 BC. It is a collection of definitions, postulates, propositions (theorems and constructions), and mathematical proofs of the propositions. The books cover plane and solid Euclidean geometry, elementary number theory, and incommensurable lines. Elements is the oldest extant large-scale deductive treatment of mathematics. It has proven instrumental in the development of logic and modern science, and its logical rigor was not surpassed until the 19th century.

We start with a basic question in logic:

Question:

You are a prisoner in a room with 2 doors and 2 guards. One of the doors will guide you to freedom and behind the other is a hangman –you don’t know which is which.

One of the guards always tells the truth and the other always lies. You don’t know which one is the truth-teller or the liar either. However both guards know each other.

You have to choose and open one of these doors, but you can only ask a single question to one of the guards.

What do you ask so you can pick the door to freedom?

Answer

If you asked the truth-guard, the truth-guard would tell you that the liar-guard would point to the door that leads to death.

If you asked the liar-guard, the liar-guard would tell you that the truth-guard would point to the door that leads to death.

Therefore, no matter who you ask, the guards tell you which door leads to death, and therefore you can pick the other door.