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MATH 3181 Section 001 Fall, 1996
HOMEWORK SET 2
Bee and hive are undefined terms. They are related by the following set of Axioms
- P1:
- Every hive is a collection of bees.
- P2:
- Any two distinct hives have one and only one bee in common.
- P3:
- Every bee belongs to two and only two hives.
- P4:
- There are exactly four hives.
Prove the following Propositions.
- There are exactly six bees.
- There are exactly three bees in each hive.
- For each bee there is exactly one other bee not in the same hive with it.
Geometry Problems
- If the point B lies between the points A and C and the point E lies between
the points D and F and if
and 
, prove that 
- Given
, prove that for any point B between A and C there is a
unique point E between D and F such that 
.
David C Royster
Mon Sep 9 21:01:51 EDT 1996