Advertisements
Advertisements
प्रश्न
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.)
Advertisements
उत्तर
Axiom 5 states that the whole is greater than the part. This axiom is known as a universal truth because it holds true in any field and not just in the field of mathematics. Let us take two cases − one in the field of mathematics and one other than that.
Case I
Let t represent a whole quantity, and only a, b, and c are 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
Let us consider the 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. This is true for anything in any part of the world and is thus a universal truth.
APPEARS IN
संबंधित प्रश्न
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.
How many lines can be drawn through both of the given points?
Boundaries of solids are ______.
Greek’s emphasised on ______.
Which of the following needs a proof?
Solve the following question using appropriate Euclid’s axiom:
Look at the figure. Show that length AH > sum of lengths of AB + BC + CD.
Solve the following question using appropriate Euclid’s axiom:
In the following figure, we have ∠1 = ∠2, ∠2 = ∠3. Show that ∠1 = ∠3.
Solve the following question using appropriate Euclid’s axiom:
In the following figure, we have ∠ABC = ∠ACB, ∠3 = ∠4. Show that ∠1 = ∠2.
Solve the following question using appropriate Euclid’s axiom:
In the following figure, we have AC = DC, CB = CE. Show that AB = DE.
The following statement is true or false? Give reason for your answer.
If two circles are equal, then their radii are equal.
