Prove or disprove the following Functional dependencies. Proof should use Armstrong's inference rules (IR1 through IR3 only) and disproof should be through a counterexample.

a) {X --> Y, Z --> W} |= {XZ --> YW}

b) {X --> Y, X --> W, WY --> Z} |= {X --> Z}

c) {XY --> Z, Y --> W} |= {XW --> Z}

d) {XY --> Z, Z --> X} |= {Z --> Y}