# Ex.5.1 Q7 Introduction to Euclids Geometry Solution - NCERT Maths Class 9

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## Question

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.)

## Text Solution

Reasoning:

Axiom $$5$$ – “The whole is greater than the part.”

steps:

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.

i). Let us consider a line segment $$AB$$. Mark two points $$P$$ and $$Q$$ on it. $$AB$$ is a whole part. It is divided into three parts: $$AP,\;PQ,\;QB.$$

\begin{align} A B &= A P + P Q + Q B \\ A B &> A P \\ A B &> P Q \\ A B &> Q B \end{align}

ii). Bangalore is a part of Karnataka which means that Karnataka is larger than Bangalore. i.e. Karnataka $$>$$ Bangalore.

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

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