Question

Consider the two ‘postulates’ given below:

(i) Given any two distinct points A and B, there exists a third point C, which is between A and B.

(ii) There exists 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.

Answer 1

There are various undefined terms in the given postulates.

The given postulates are consistent because they refer to two different situations. Also, it is impossible to deduce any statement that contradicts any well known axiom and postulate.

These postulates do not follow from Euclid’s postulates. They follow from the axiom,

“Given two distinct points, there is a unique line that passes through them”.