1. Given R(dnumber, dname, pname, pnumber, plocation), and the following functional dependencies:

Pnumber --> pname

Pnumber --> plocation

Dnumber --> dname

We decompose R into two relations R1(dnumber, dname) and R2(pname, pnumber, plocation, dnumber). Does this decomposition have the lossless join property? Show your steps to achieve the answer.

(This one does not need to be typed.)

2. Given R(x,y, z, w, k, f, q) and the following functional dependencies:

Fd1: x {z,w}

Fd2: y {k,f}

Decompose R into 3rd normal form with both dependency preservation property and loss-less join property.

(This one must be typed)

3. Given R(a,b, c,d,e,f,g). There are two keys: (a,b) and d. Given the following functional dependency: F = { {a,b} {c,d,e,f,g}, d {a,b, c, e,f,g}, f a}. Decompose R into BCNF.

(This one must be typed)

1. Given R(dnumber, dname, pname, pnumber, plocation), and the following functional dependencies: Pnumber-> pname Dnumber dname We decompose R into two relations R1(dnumber, dname) and R2(pname, pnumber, plocation, dnumber). Does this decomposition have the lossless join property? Show your steps to achieve the answer (This one does not need to be typed.) 2. Given R(X.y, z, w, k, f, q) and the following functional dependencies: Decompose R into 3rd normal form with both dependency preservation property and loss-less join property (This one must be typed) 3. Given R(ab, c de.f.g). There are two keys: (a.b) and d. Given the following functional Decompose R into dependency: F = { {ab}-) {c.d.eate, d-) a,b, c, efg), f > a} . BCNF (This one must be typed) 1. Given R(dnumber, dname, pname, pnumber, plocation), and the following functional dependencies: Pnumber-> pname Dnumber dname We decompose R into two relations R1(dnumber, dname) and R2(pname, pnumber, plocation, dnumber). Does this decomposition have the lossless join property? Show your steps to achieve the answer (This one does not need to be typed.) 2. Given R(X.y, z, w, k, f, q) and the following functional dependencies: Decompose R into 3rd normal form with both dependency preservation property and loss-less join property (This one must be typed) 3. Given R(ab, c de.f.g). There are two keys: (a.b) and d. Given the following functional Decompose R into dependency: F = { {ab}-) {c.d.eate, d-) a,b, c, efg), f > a} . BCNF (This one must be typed)