Prove or disprove the following proposed inference rules for functional dependencies. A proof should be made by using the reflexive, augmentation, transitive, decomposition, union, and pseudotransitive rules or 'given'. A disproof should be performed by demonstrating a relation instance that satisfies the conditions and functional dependencies on the left hand side of the proposed rule but does not satisfy the dependencies on the right hand side. No other form of dispoof will be accepted.

a. {Y ? X, Z ? X} ? {Z ? Y}

b. {Z ? X, XZ ? Y} ? {Z ? Y}

c. {XZ ? Y, Y ? X} ? {Y ? Z}

d. {XY ? WZ, Y ? Z} ? {X ? W}

e. {X ? WZ, W ? YZ} ? {X ? YZ}

f. {Y ? XZ, Z ? W} ? {Y ? XWZ}

g. {X ? Z, X ? W, WZ ? Y} ? { X ? Y }

h. {VY ? XZ, W ? UY, U ? Z} ? {VW ? X}