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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