Consider two ‘postulates’ given below:
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.
Answer
Undefined terms in the postulates:
→ Many points lie in a plane. But here it is not given about the position of the point C whether it lies on the line segment joining AB or not.
→ Also, there is no information about the plane whether the points are in same plane or not.
Yes, these postulates are consistent when we deal with these two situation:
(i) Point C is lying in between and on the line segment joining A and B.
(ii) Point C not lies on the line segment joining A and B.
No, they don't follow from Euclid’s postulates. They follow the axioms.
