Note: Nathan mentioned that only Section 1 (Properties of Relations) would be examined, while Section 2 was supplementary information for interest only.
Relations and Expressive Adequacy
SECTION 1: PROPERTIES OF RELATIONS (Examinable Material)
1. Basic Concepts of Relations
Arity of Relations
Defines how many "places" or "gaps" a relation has
Examples:
One place (properties): "is a dog", "is red"
Binary (two places): "is taller than", "loves"
Three places: "is between"
Four or more places: possible but less common
Most relations discussed are binary relations
Properties are technically just one-place relations
Converse Relations
Definition: The "opposite" direction of a relation
Formal definition: For relation R, its converse R* exists when xRy implies yR*x
Examples:
"Is taller than" → converse is "is shorter than"
"Loves" → converse is "is loved by"
Philosophical debate exists about whether relations and their converses are truly distinct
Can be understood as same ordered pairs flipped around