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Question
Consider two ‘postulates’ given below:-
- Given any two distinct points A and B, there exists a third point C which is in between A and B.
- 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.
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Solution
Yes, these postulates include undefined terms like 'point and line'. Furthermore, these postulates are consistent because they deal with two distinct situations:
- States that given two points, A and B, a point C exists on the line that connects them. Whereas
- States that given points A and B, you can select a point C that is not on the line that connects them.
No, these postulates are not derived from Euclid's postulates but rather from the axiom, "Given two distinct points, there is a unique line that passes through them."
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