Recall from Example 8.15 the “betweenness” relation, defined as the ternary relation B :=  hx, y, zi ∈ R3 : x ≤ y ≤ z or x ≥ y ≥ z . Show how to construct B using only ≤, the relation operators (−1 ,...

Recall from Example 8.15 the “betweenness” relation, defined as the ternary relation B :=  hx, y, zi ∈ R3 : x ≤ y ≤ z or x ≥ y ≥ z . Show how to construct B using only ≤, the relation operators (−1 , ◦, join, select, project), and standard set-theoretic operations (∪, ∩, ∼, −).

Example 8.15

8.15 S ◦ R