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I'm new to writing proofs and am working with proving finite geometry systems. I'm not sure how I should answer this one. Using the four point finite geometry system: prove that there exists a set of lines in the four point geometry that contains all the points of the geometry.

  • Axiom 1: there exists four points
  • Axiom 2: any two distinct points have exactly one line on them
  • Axiom 3: each line is on exactly two points
Gabby
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1 Answers1

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Hint

Let $P=\{a,b,c,d\}$ such that $a, b , c, d$ are distinct points. Each line is a subset of $P$.

Let $L$ be the set of lines on $P$.

Show that there exists $S\subseteq L$, with a line for each distinct pair of points in $P$. Then show that $S$ is the required set.

Dan Christensen
  • 14,529