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:
Axiom 5 of Euclid's Axioms 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.
- Bangalore is a part of Karnataka which means that Karnataka is larger than Bangalore. i.e. Karnataka > Bangalore.
- 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.
☛ Check: NCERT Solutions Class 9 Maths Chapter 5
Video Solution:
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.)
NCERT Solutions Class 9 Maths Chapter 5 Exercise 5.1 Question 7
Summary:
Euclid's axiom 5 - “The whole is greater than the part” is known as a universal truth because it holds true in any field of mathematics and in other disciplinarians of science as well.
☛ Related Questions:
- If a point C lies between two points A and B such that AC = BC, then prove that AC = 1/2 AB. Explain by drawing the figure.
- In Question 4, point C is called a mid-point of line segment AB. Prove that every line segment has one and only one mid-point.
- In Fig. 5.10, if AC = BD, then prove that AB = CD.
- Consider two 'postulates' given below:i) Given any two distinct points A and B there exists a third point C which is in between A and B.ii) There exist at least three points that are not on the same line.Do these postulates contain any undefined terms? Are these postulates consistent? Do they follow from Euclid’s postulates? Explain.