Example of MVF and CFR:
F = Domain Female; M = CoDomain Male.
R = Relation HusbandOf from F to M
Assume the relation is fully defined
1. Relation as Multi-Valued Function (MVF)
- y = R(x) is “y = HusbandOf(x)” (y ? M).
- R(x) is generally multi-valued:
- Example: IsOrWasHusbandOf(y,x)?.
- In general, R maps X into PowerSet(Y).
2. Relation as Characteristic Function:
- CFR(y, x) is “IsHusbandOf(x, y)?”.
- CFR maps MxF into {TRUE, FALSE}.
y ? HusbandOf(x) iff IsHusbandOf(y, x) is True.
- Alternate way to write CFR: Y.IsHusbandOf.X.