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 IR1
through IR3. A disproof should be done by demonstrating a relation instance that
satisfies the conditions and functional dependencies in the left hand side of the
inference rule but do not
satisfy the conditions or dependencies in the right hand side.
(a) {W ->Y, X ->Z} |= {WX ->Y }
(b) {X ->Y} and Z subset-of Y |= { X ->Z }
(c) { X ->Y, X ->W, WY ->Z} |= {X ->Z}
(d) {XY ->Z, Y ->W} |= {XW ->Z}
(e) {X ->Z, Y ->Z} |= {X ->Y}
(f) {X ->Y, XY ->Z} |= {X ->Z}