Prove or disprove the following inference rules for functional dependencies. A
proof can be made either by a proof argument or by using inference rules lRl
through IR3.A disproof should be performed by demonstrating a relation instance
that satisfies the conditions and functional dependencies in the left-hand side of
the inference rule but does not satisfy the dependencies in the right-hand side.
a. W -7 Y, X -7 Z F WX -7 Y
b. X-7 Y and Y :2 Z F X -7 Z
c. X -7 Y, X -7 v, WY -7 Z F X -7 Z
d. XY-7 Z, Y -7 W F XW -7 Z
e. X -7 Z, Y -7 Z F X -7 Y
f. X -7 Y, XY -7 Z F X -7 Z
g. IX -7 Y, Z -7 W} F XZ -7 YW
h. XY -7 Z, Z -7 X F Z -7 Y
i. X -7 Y, Y -7 Z F X -7 YZ
j. XY -7 Z, Z -7 W F X -7 W
10.19. Consider the following two sets of functional dependencies: F = A -7 C, AC -7
D, E -7 AD, E -7 H and G = A -7 CD, E -7 AH. Check whether they are
equivalent.