Deduce Linear Order from Relations

​
objects
figures
letters
digits
number of elements
3
4
5
maximum number
of statements
3
check solution
new problem
A is beside C.
False
A is to the left of B.
False
A list of objects is given. The objects can be figures, letters or digits. Write down the arrangement of the objects to appear in the row of red squares so that the given statements are true, then check your solution. The statement can involve binary relations "left of," "right of" and "besides" and ternary relations like "A is between B and C" and "1 is equally distant from 2 and 3."

Details

If A is between B and C, A is not necessarily adjacent to B or C.
M. Piery has shown that a ternary relation, that of a point being equally distant from two other points, can be used as the only primitive notion of Euclidean geometry of two or more dimensions[1, p. 68].

References

[1] R. M. Robinson, "Binary Relations as Primitive Notions in Elementary Geometry: The Axiomatic Method with Special Reference to Geometry and Physics," in Proceedings of an International Symposium Held at the University of California, Berkeley, December 26, 1957–January 4, 1958, Amsterdam: North-Holland Publishing Company, 1959 pp. 68–85. doi:10.1017/S0022481200092690.

External Links

False (Wolfram MathWorld)
True (Wolfram MathWorld)
Some Simple Logic Problems
Logic with Logicians
Logic Problems for Elementary Students

Permanent Citation

Izidor Hafner
​
​"Deduce Linear Order from Relations"​
​http://demonstrations.wolfram.com/DeduceLinearOrderFromRelations/​
​Wolfram Demonstrations Project​
​Published: July 30, 2018