Relational Algebra and Calculus 29

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1 Relational Algebra and Calculus Find the names of suppliers who supply some red part. 2. Find the sids of suppliers who supply some red or green part. 3. Find the sids of suppliers who supply some red part or are at 221 Packer Street. 4. Find the sids of suppliers who supply some red part and some green part. 5. Find the sids of suppliers who supply every part. 6. Find the sids of suppliers who supply every red part. 7. Find the sids of suppliers who supply every red or green part. 8. Find the sids of suppliers who supply every red part or supply every green part. 9. Find pairs of sids such that the supplier with the first sid charges more for some part than the supplier with the second sid. 10. Find the pids of parts supplied by at least two different suppliers. 11. Find the pids of the most expensive parts supplied by suppliers named Yosemite Sham. 12. Find the pids of parts supplied by every supplier at less than $200. (If any supplier either does not supply the part or charges more than $200 for it, the part is not selected.) Answer 4.3 In the answers below RA refers to Relational Algebra, refers to Tuple Relational Calculus and refers to Domain Relational Calculus. 1. RA π sname (π sid ((π pid σ color= red Parts) C atalog) Suppliers) {T T1 Suppliers( X Parts(X.color = red Y Catalog (Y.pid = X.pid Y.sid = T 1.sid)) T.sname = T 1.sname)} { Y X, Y, Z Suppliers P, Q, R( P, Q, R Parts R = red I,J,K( I,J,K Catalog J = P I = X))}

2 30 Chapter 4 SELECT S.sname FROM Suppliers S, Parts P, Catalog C WHERE P.color= red AND C.pid=P.pid AND C.sid=S.sid 2. RA π sid (π pid (σ color= red color= green Parts) catalog) {T T1 Catalog( X Parts((X.color = red X.color = green ) X.pid = T 1.pid) T.sid = T 1.sid)} { X X, Y, Z Catalog A, B, C( A, B, C Parts (C = red C = green ) A = Y )}, Parts P WHERE (P.color = red OR P.color = green ) AND P.pid = C.pid 3. RA ρ(r1,π sid ((π pid σ color= red Parts) C atalog)) ρ(r2,π sid σ address= 221P ackerstreet Suppliers) R1 R2 {T T1 Catalog( X Parts(X.color = red X.pid = T 1.pid) T.sid = T 1.sid) T 2 Suppliers(T 2.address = 221P ackerstreet T.sid = T 2.sid)} { X X, Y, Z Catalog A, B, C( A, B, C Parts C = red A = Y ) P, Q( X, P, Q Suppliers Q = 221P ackerstreet )}

3 Relational Algebra and Calculus 31 SELECT S.sid FROM Suppliers S WHERE S.address = 221 Packer street OR S.sid IN (, Catalog C WHERE P.color= red AND P.pid = C.pid ) 4. RA ρ(r1,π sid ((π pid σ color= red Parts) C atalog)) ρ(r2,π sid ((π pid σ color= green Parts) C atalog)) R1 R2 {T T1 Catalog( X Parts(X.color = red X.pid = T 1.pid) T 2 Catalog( Y Parts(Y.color = green Y.pid = T 2.pid) T 2.sid = T 1.sid) T.sid = T 1.sid)} { X X, Y, Z Catalog A, B, C( A, B, C Parts C = red A = Y ) P, Q, R( P, Q, R Catalog E,F,G( E,F,G Parts G = green E = Q) P = X)}, Catalog C WHERE P.color = red AND P.pid = C.pid AND EXISTS ( SELECT P2.pid 2, Catalog C2 WHERE P2.color = green AND C2.sid = C.sid AND P2.pid = C2.pid ) 5. RA (π sid,pid Catalog)/(π pid Parts) {T T1 Catalog( X Parts( T2 Catalog (T 2.pid = X.pid T 2.sid = T 1.sid)) T.sid = T 1.sid)}

4 32 Chapter 4 { X X, Y, Z Catalog A, B, C Parts ( P, Q, R Catalog(Q = A P = X))} WHERE NOT EXISTS (SELECT P.pid WHERE NOT EXISTS (SELECT C1.sid 1 WHERE C1.sid = C.sid AND C1.pid = P.pid)) 6. RA (π sid,pid Catalog)/(π pid σ color= red Parts) {T T 1 Catalog( X Parts(X.color red T 2 Catalog(T2.pid = X.pid T 2.sid = T 1.sid)) T.sid = T 1.sid)} { X X, Y, Z Catalog A, B, C Parts (C red P, Q, R Catalog(Q = A P = X))} WHERE NOT EXISTS (SELECT P.pid WHERE P.color = red AND (NOT EXISTS (SELECT C1.sid 1 WHERE C1.sid = C.sid AND C1.pid = P.pid))) 7. RA (π sid,pid Catalog)/(π pid σ color= red color= green Parts)

5 Relational Algebra and Calculus 33 {T T 1 Catalog( X Parts((X.color red X.color green ) T2 Catalog (T 2.pid = X.pid T 2.sid = T 1.sid)) T.sid = T 1.sid)} { X X, Y, Z Catalog A, B, C Parts ((C red C green ) P, Q, R Catalog (Q = A P = X))} WHERE NOT EXISTS (SELECT P.pid WHERE (P.color = red OR P.color = green ) AND (NOT EXISTS (SELECT C1.sid 1 WHERE C1.sid = C.sid AND C1.pid = P.pid))) 8. RA ρ(r1, ((π sid,pid Catalog)/(π pid σ color= red Parts))) ρ(r2, ((π sid,pid Catalog)/(π pid σ color= green Parts))) R1 R2 {T T1 Catalog(( X Parts (X.color red Y Catalog(Y.pid = X.pid Y.sid = T 1.sid)) Z Parts(Z.color green P Catalog (P.pid = Z.pid P.sid = T 1.sid))) T.sid = T 1.sid)} { X X, Y, Z Catalog ( A, B, C Parts (C red P, Q, R Catalog(Q = A P = X)) U, V, W Parts(W green M,N,L Catalog (N = U M = X)))}

6 34 Chapter 4 WHERE (NOT EXISTS (SELECT P.pid WHERE P.color = red AND (NOT EXISTS (SELECT C1.sid 1 WHERE C1.sid = C.sid AND C1.pid = P.pid)))) OR ( NOT EXISTS (SELECT P1.pid 1 WHERE P1.color = green AND (NOT EXISTS (SELECT C2.sid 2 WHERE C2.sid = C.sid AND C2.pid = P1.pid)))) 9. RA ρ(r1, Catalog) ρ(r2, Catalog) π R1.sid,R2.sid (σ R1.pid=R2.pid R1.sid R2.sid R1.cost>R2.cost (R1 R2)) {T T 1 Catalog( T 2 Catalog (T 2.pid = T 1.pid T 2.sid T 1.sid T 2.cost < T 1.cost T.sid2=T2.sid) T.sid1=T1.sid)} { X, P X, Y, Z Catalog P, Q, R ( P, Q, R Catalog Q = Y P X R<Z)} SELECT C1.sid, C2.sid 1, Catalog C2 WHERE C1.pid = C2.pid AND C1.sid C2.sid AND C1.cost > C2.cost

7 Relational Algebra and Calculus RA ρ(r1, Catalog) ρ(r2, Catalog) π R1.pid σ R1.pid=R2.pid R1.sid R2.sid (R1 R2) {T T1 Catalog( T 2 Catalog (T 2.pid = T 1.pid T 2.sid T 1.sid) T.pid = T 1.pid)} { X X, Y, Z Catalog A, B, C ( A, B, C Catalog B = Y A X)} SELECT C.pid WHERE EXISTS (SELECT C1.sid 1 WHERE C1.pid = C.pid AND C1.sid C.sid ) 11. RA ρ(r1,π sid σ sname= YosemiteSham Suppliers) ρ(r2,r1 Catalog) ρ(r3,r2) ρ(r4(1 sid, 2 pid, 3 cost),σ R3.cost<R2.cost (R3 R2)) π pid (R2 π sid,pid,cost R4) {T T1 Catalog( X Suppliers (X.sname = YosemiteSham X.sid = T 1.sid) ( S Suppliers (S.sname = YosemiteSham Z Catalog (Z.sid = S.sid Z.cost > T 1.cost))) T.pid = T 1.pid) { Y X, Y, Z Catalog A, B, C ( A, B, C Suppliers C = YosemiteSham A = X) ( P, Q, R( P, Q, R Suppliers R = YosemiteSham I,J,K( I,J,K Catalog(I = P K>Z))))}

Tuple Relational Calculus

Tuple Relational Calculus Université de Mons (UMONS) May 14, 2018 Motivation S[S#, SNAME, STATUS, CITY] P[P#, PNAME, COLOR, WEIGHT, CITY] SP[S#, P#, QTY)] Get all pairs of city names such that a supplier