Using Armstrong's axioms of functional dependency, derive the following rule:
{x - y, wy - z} |= xw - z

(Note: x - ...

Question

Using Armstrong's axioms of functional dependency, derive the following rule:
{x -> y, wy -> z} |= xw -> z

(Note: x -> y denotes y is functionally dependent on x; z subset_of y denotes z is subset of y; and |= means derives).

Accepted Answer

xw -> z is derived using Augmentation on x->y (to get xw->yw) followed by Transitivity with wy->z. We have two FDs: x determines y, and wy together determine z. We need to show that xw (x combined with w) also determines z. The key insight is to augment x->y with w to get xw->yw, and then use transitivity since wy->z.

Using Armstrong's axioms of functional dependency, derive the following rule: {x -> y, wy -> z} |= xw -> z (Note: x -> y denotes y is functionally dependent on x; z subset_of y denotes z is subset of y; and |= means derives).