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zain
guest

Jan2211, 04:12 PM (EST) 

"discrete math"

axiam 1: every line is a set of points. axiam 2: for each line 'L' there is a point on 'L'. axiam 3: there exists at least 2 points. axiam 4:for every point of distinct points there is one and only one line containing these points.show that there are at least three lines. how can we prove this either by taking contrapositive of above axiams or is any direct proof can we give? 

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zain
guest

Jan2311, 04:15 PM (EST) 

2. "RE: discrete math"
In response to message #1

sorry for using 'axiam' instead of 'Axiom'. actually i got it as final assignment but the problem is that it doesn't belong to my course so i can't even guess it. so this problem drag me to this site if i get any help. thnx for bearing me.


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zain
guest

Jan2411, 08:07 AM (EST) 

5. "RE: discrete math"
In response to message #3

Finally i got these axioms in true form. these are the correct one so proceed with these. thanks for pointing out errors in my problem. axiom 1: every line is a set of points. axiom 2: for each line 'L' there is a point not on 'L'. axiom 3: there exists at least 2 points. axiom 4: for every pair of distinct points, there is one and only one line containing these points. show that there are at least three lines. so i m v8ing to hear from you people soon.


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alexb
Charter Member
2743 posts 
Jan2411, 08:15 AM (EST) 

6. "RE: discrete math"
In response to message #5

>Finally i got these axioms in true form. Good. You have to understand the problem before starting to solve it. >axiom 1: every line is a set of points. >axiom 2: for each line 'L' there is a point not on 'L'. >axiom 3: there exists at least 2 points. >axiom 4: for every pair of distinct points, there is one and >only one line containing these points. > >show that there are at least three lines. >so i m v8ing to hear from you people soon. This is not a nice thing to say. We people have our schedules  sometimes pretty tense. Just say thank you. Please try to think. Draw as you do and answer the three questions below: What does #3 say? What does #4 add to this? What does #2 add to this?


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zain
guest

Jan2511, 08:11 AM (EST) 

7. "RE: discrete math"
In response to message #6

oh! i see. so by A3 we have at least 2 points let call them a, b. and they are distinct correct.? now A4 says these 2 points lies on only one line. but by A2 there exists another line not containing point b and again by A2 another line not containing point a. So according to my consideration this geometry has at least three lines.is this ok or not. thanks in advance. 

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alexb
Charter Member
2743 posts 
Jan2511, 08:21 AM (EST) 

8. "RE: discrete math"
In response to message #7

>oh! i see. >so by A3 we have at least 2 points let call them a, b. and >they are distinct correct.? By A3, there are two distinct points. It's up to you to pick a and b distinct. A3 only says that you can do that. So do. >now A4 says these 2 points lies on only one line. Essentially they lie on a line, say L. That L is unique is not important at this point. >but by A2 there exists another line not containing point b >and again by A2 another line not containing point a. >So according to my consideration this geometry has at least >three lines. By A2, there is a point c not on L. This makes c distinct from a and b because both are on L. By A4, there is a line La through c and a and line Lb through c and b. The three lines L, La, Lb must be distinct because otherwise the three points a, b, c would lie on a single line but, since c is not on L, the line would be different from L but still pass through a and b. This would make two lines through a and b, contradicting uniqueness in A3. > >is this ok or not. >thanks in advance.


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