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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.

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.

Grade:12th pass

1 Answers

Pawan Prajapati
askIITians Faculty 6228 Points
3 months ago
There are several undefined terms which the student should list. They are consistent, because they deal with two different situations: (i) Says that given two points A and B, there is a point c lying on the line in between them. (il) Says that given A and B, you can take C not lying on the line through A and B. These 'p.ostulates' do not follow from Euclid's .postulates.

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