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CBSE Class 9 Mathematics Question 7 of 7

Introduction to Euclid's Geometry — Question 7

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Question 7

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).

Answer

Axiom 5 states that :

'Whole is always greater than its part'. This is a 'universal truth' because it holds true in any field of mathematics and in other disciplinarians of science as well.

Let us take two cases: one in the field of mathematics and one other than that.

Case 1 — Let t represent a whole quantity and only a, b, c are parts of it.

Such that :

t = a + b + c

Clearly, t will be greater than all of its parts a, b and c. Therefore, it is rightly said that the whole is greater than the part.

Case 2 — Let us consider continent Asia. Then, let us consider a country India which belongs to Asia. India is a part of Asia and it can also be observed that Asia is greater than India. That is why we can say that the whole is greater than the part.