Consider the following relations P ( X , Y , Z ) , Q ( X , Y , T ) P(X,Y,Z), Q(X,Y,T) P ( X , Y , Z ) , Q ( X , Y , T ) R ( Y , V ) R(Y,V) R ( Y , V )
X Y Z X1 Y1 Z1 X1 Y1 Z2 X2 Y2 Z2 X2 Y4 Z4 Table: P X Y T X2 Y1 2 X1 Y2 5 X1 Y1 6 X3 Y3 1 Table: Q Y V Y1 V1 Y3 V2 Y2 V3 Y2 V2 Table: R \overset{\textbf{Table: P}}{\begin{array}{|l|l|l|} \hline \textbf{X} & \textbf{Y} & \textbf{Z} \\\hline \text{X1} & \text{Y1} & \text{Z1} \\\hline \text{X1} & \text{Y1} & \text{Z2} \\\hline \text{X2} & \text{Y2} & \text{Z2} \\\hline \text{X2} & \text{Y4} & \text{Z4} \\\hline \end{array}} \qquad \overset{\textbf{Table: Q}}{\begin{array}{|l|l|l|} \hline \textbf{X} & \textbf{Y} & \textbf{T} \\\hline \text{X2} & \text{Y1} & 2 \\\hline \text{X1} & \text{Y2} & 5 \\\hline \text{X1} & \text{Y1} & 6 \\\hline \text{X3} & \text{Y3} & 1 \\\hline \end{array}} \qquad \overset{\textbf{Table: R}}{\begin{array}{|l|l|} \hline \textbf{Y} & \textbf{V} \\\hline \text{Y1} & \text{V1} \\\hline \text{Y3} & \text{V2} \\\hline \text{Y2} & \text{V3} \\\hline \text{Y2} & \text{V2} \\\hline \end{array}} X X1 X1 X2 X2 Y Y1 Y1 Y2 Y4 Z Z1 Z2 Z2 Z4 Table: P X X2 X1 X1 X3 Y Y1 Y2 Y1 Y3 T 2 5 6 1 Table: Q Y Y1 Y3 Y2 Y2 V V1 V2 V3 V2 Table: R How many tuples will be returned by the following relational algebra query?
Π x ( σ ( P . Y = R . Y ∧ R . V = V 2 ) ) ( P × R ) ) – Π x ( σ ( Q . Y = R . Y ∧ Q . T > 2 ) ) ( Q × R ) ) \Pi_x (\sigma_{(P.Y=R.Y \wedge R.V=V2))} (P \times R)) – \Pi_x (\sigma_{(Q.Y = R.Y \wedge Q.T>2))} (Q \times R)) Π x ( σ ( P . Y = R . Y ∧ R . V = V 2 )) ( P × R )) – Π x ( σ ( Q . Y = R . Y ∧ Q . T > 2 )) ( Q × R ))