Question

Consider 2 postulates given below (i) given any distinct points A and B, there exists a 3rd point C which is in between A and B (ii) there exist at least 3points that are not one the same line. Are these postulates consistent? Do they follow from Euclid's postulates Explain Please answer fastly

Answer 1

Solution:

There are so many undefined terms which should be listed they are consistent because they deal with two different situations which are as follows:

1.

If two points A and B are given then there exist a third point C which is in between A and B.

2.

If two points A and B are given then we can take a point C which do not lie on the line passing through the points A and B . Thus these points do not contradict each other.

These postulates do not follow Euclid's postulates. However they follow axiom. Euclid postulate 1 axiom states that through two distinct points there is a unique lines that passes through them.

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