Prove or disprove that the following inference rules for functional dependencies. A proof can be made by using inference rules IR1 through IR3. A disproof should be done by showing a relational instance that refutes 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} andImage for Question: Prove or disprove the following inference rules for functional dependencies. A proof can be made eit|= {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}