Why is Axiom 5, in the list of Euclid’s axioms, considered a ‘universal truth’? (Note that the question is not about the fifth postulate.)

Axiom 5 states that - “The whole is greater than the part.”

This axiom is known as a universal truth because it holds true in any field of mathematics and in other disciplinarians of science as well.

Let us consider a line segment AB. Mark two points P and Q on AB is a whole part.

It is divided into three parts: AP, PQ, QB.

AB = AP + PQ + QB

Thus, we see that

AB > AP

AB > PQ

AB > QB

Hence, AB (whole) is greater than its parts i.e, AP, PQ, and QB.

Let's take some practical facts to understand this.

1. Lucknow is a part of Uttar Pradesh which means that Uttar Pradesh is larger than Lucknow. i.e. Uttar Pradesh > Lucknow  .
2. India is a part of the world which concludes the world is larger than India. Here the world is a whole whereas, India is just a part of it.

Therefore, it is true that the whole is greater than the part that is considered as universal truth.