3. 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.
There are various undefined terms in the given postulates.:
1) There is no information given about the plane whether the points are in the same plane or not.
2) There is the infinite number of points lie in a plane. But here the position of the point C has not specified whether it lies on the line segment joining AB or not.
Yes, these postulates are consistent when we deal with these two situations:
(i) Point C is lying in between and on the line segment joining A and B.
(ii) Point C does not lie on the line segment joining A and B.
No, they don’t follow from Euclid’s postulates. They follow the axioms.