**Figure 5.7: Result of a Theta-Outerjoin**The table illustrates the result of a theta-outerjoin operation, with columns labeled $A$, $U.B$, $U.C$, $V.B$, $V.C$, and $D$. The data is organized as follows:- Row 1: 4, 5, 6, 2, 3, 10- Row 2: 4, 5, 6, 2, 3, 11- Row 3: 7, 8, 9, 2, 3, 10- Row 4: 7, 8, 9, 2, 3, 11- Row 5: 1, 2, 3, ⊥, ⊥, ⊥- Row 6: ⊥, ⊥, ⊥, 6, 7, 12**5.2.8 Exercises for Section 5.2****Exercise 5.2.1:** Here are two relations:$R(A, B): \{(0, 1), (2, 3), (0, 1), (2, 4), (3, 4)\}$$S(B, C): \{(0, 1), (2, 4), (2, 5), (3, 4), (0, 2), (3, 4)\}$Compute the following: a) $\pi_{A+B,A^2,B^2}(R);$b) $\pi_{B+1,C-1}(S);$c) $\tau_{B,A}(R);$d) $\tau_{B,C}(S);$e) $\delta(R);$f) $\delta(S);$g) $\gamma_{A, \text{SUM}(B)}(R);$h) $\gamma_{B, \text{AVG}(C)}(S);$i) $!\gamma_{A}(R);$j) $\gamma_{A, \text{MAX}(C)}(R \bowtie S);$k) $R \bowtie_L S;$l) $R \bowtie_R S;$m

Given: a. Compute πA+B, A2, B2R A B A+B A2 B2 0 1 1 0 1 2 3 5 4 9 0 1 1 0 1 2 4 6 4 16…

Exercise 5.2.1: Here are two relations: R(A, B): {(0,1), (2,3), (0,1), (2,4), (3,4)} S(B,C): {(0,1), (2,4), (2,5), (3,4), (0,2), (3, 4)} Compute the following: а) ПА+В,А?, В2(R); b) тв+1,с-1(S); с) тв, A(R);

Exercise 5.2.1: Here are two relations: R(A, B): {(0,1), (2,3), (0,1), (2,4), (3,4)} S(B,C): {(0,1), (2,4), (2,5), (3,4), (0,2), (3, 4)} Compute the following: а) ПА+В,А?, В2(R); b) тв+1,с-1(S); с) тв, A(R);

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Question

**Figure 5.7: Result of a Theta-Outerjoin**

The table illustrates the result of a theta-outerjoin operation, with columns labeled $A$, $U.B$, $U.C$, $V.B$, $V.C$, and $D$. The data is organized as follows:

- Row 1: 4, 5, 6, 2, 3, 10
- Row 2: 4, 5, 6, 2, 3, 11
- Row 3: 7, 8, 9, 2, 3, 10
- Row 4: 7, 8, 9, 2, 3, 11
- Row 5: 1, 2, 3, ⊥, ⊥, ⊥
- Row 6: ⊥, ⊥, ⊥, 6, 7, 12

**5.2.8 Exercises for Section 5.2**

**Exercise 5.2.1:** Here are two relations:

$R(A, B): \{(0, 1), (2, 3), (0, 1), (2, 4), (3, 4)\}$

$S(B, C): \{(0, 1), (2, 4), (2, 5), (3, 4), (0, 2), (3, 4)\}$

Compute the following:

a) $\pi_{A+B,A^2,B^2}(R);$

b) $\pi_{B+1,C-1}(S);$

c) $\tau_{B,A}(R);$

d) $\tau_{B,C}(S);$

e) $\delta(R);$

f) $\delta(S);$

g) $\gamma_{A, \text{SUM}(B)}(R);$

h) $\gamma_{B, \text{AVG}(C)}(S);$

i) $!\gamma_{A}(R);$

j) $\gamma_{A, \text{MAX}(C)}(R \bowtie S);$

k) $R \bowtie_L S;$

l) $R \bowtie_R S;$

m

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