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.)
Solution and Explanation
Axiom 5 states that the whole is greater than the part. This axiom is a universal truth because it holds true in any field, and not just in mathematics. Let us take two cases – one in the field of mathematics, and one in another field.
Case I: Mathematical Example
Let \( t \) represent a whole quantity and let \( a \), \( b \), and \( c \) represent parts of it.
\[ t = a + b + c \]
Clearly, \( t \) will be greater than all its parts \( a \), \( b \), and \( c \). Therefore, it is rightly said that the whole is greater than the part.
Case II: Geographical Example
Let us consider the continent Asia. Then, let us consider the country India, which belongs to Asia. India is a part of Asia, and it can be observed that Asia is greater than India. That is why we can say that the whole is greater than the part.
This is true for anything in any part of the world and is thus a universal truth.
Top Questions on Euclid’s Definitions, Axioms and Postulates
Which of the following statements are true and which are false? Give reasons for your answers.
(i) Only one line can pass through a single point.
(ii) There are an infinite number of lines which pass through two distinct points.
(iii) A terminated line can be produced indefinitely on both the sides.
(iv) If two circles are equal, then their radii are equal.
(v) In Fig., if AB = PQ and PQ = XY, then AB = XY
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