Assume that W, X, Y, Z are single attributes. For each case below, give a true or false answer for each of the following question. Explain your answer (by means of counter-examples, Armstrong Axioms, computing the attribute closure, etc.)

1. {W Y,X Z} implies WXY;

2. {X Y, X W,WY Z} implies X Z;

3. {XYZ, ZX} implies ZY;

4. {XY Z,YW} implies XWZ;

5. {X Z,YZ} implies XY;

6. {XY Z} implies {X Z,YZ};

7. {XZ, Y Z} implies XYZ;

8. {XY Z, ZW} implies XW;