a. Proof: Consider the expression given below: Π A (r − s) and Π A (r)−Π A (s) Assume, r = {(1, 2)}, and s = {(1, 3)}...

Question

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Answer 1

Expert Solution & Answer

Chapter 16, Problem 3PE

Explanation of Solution

a.

Proof:

Consider the expression given below:

Π_A(r − s) and Π_A(r)−Π_A(s)

Assume, r = {(1, 2)}, and s = {(1, 3)}...

Explanation of Solution

b.

Proof:

Consider the expression given below:

σ_B<4( _Aγmax(B) as B^(r)) and _Aγmax(B) as B^(σ_B<4^(r))

Assume, r = {(1, 2), (1, 5)}...

Explanation of Solution

c.

Equivalence of expressions:

“Yes”, the expressions will be equivalent if the max is replaced by min...

Explanation of Solution

d.

Proof:

Consider the expression given below:

(r⟖s)⟖t and r⟖(s⟖t)

Assume, r = {(1, 2)}, s = {(2, 3)}, t = {(1, 4)}...

Explanation of Solution

e.

Expression:

Proof:

Consider the expression given below:

σθ(E1⟕E2) and E1⟕σθ(E2)

Let R be of the schema (A, B) and S of (A, C).

Assume, r = {(1, 2)}, s = {(2, 3)} and let u be the expression C = 1...

Expert Solution & Answer

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Check out a sample textbook solution

See solution

Answer 2

Expert Solution & Answer

Chapter 16, Problem 3PE

Explanation of Solution

a.

Proof:

Consider the expression given below:

Π_A(r − s) and Π_A(r)−Π_A(s)

Assume, r = {(1, 2)}, and s = {(1, 3)}...

Explanation of Solution

b.

Proof:

Consider the expression given below:

σ_B<4( _Aγmax(B) as B^(r)) and _Aγmax(B) as B^(σ_B<4^(r))

Assume, r = {(1, 2), (1, 5)}...

Explanation of Solution

c.

Equivalence of expressions:

“Yes”, the expressions will be equivalent if the max is replaced by min...

Explanation of Solution

d.

Proof:

Consider the expression given below:

(r⟖s)⟖t and r⟖(s⟖t)

Assume, r = {(1, 2)}, s = {(2, 3)}, t = {(1, 4)}...

Explanation of Solution

e.

Expression:

Proof:

Consider the expression given below:

σθ(E1⟕E2) and E1⟕σθ(E2)

Let R be of the schema (A, B) and S of (A, C).

Assume, r = {(1, 2)}, s = {(2, 3)} and let u be the expression C = 1...

Expert Solution & Answer

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Check out a sample textbook solution

See solution

Answer 3

Expert Solution & Answer

Chapter 16, Problem 3PE

Explanation of Solution

a.

Proof:

Consider the expression given below:

Π_A(r − s) and Π_A(r)−Π_A(s)

Assume, r = {(1, 2)}, and s = {(1, 3)}...

Explanation of Solution

b.

Proof:

Consider the expression given below:

σ_B<4( _Aγmax(B) as B^(r)) and _Aγmax(B) as B^(σ_B<4^(r))

Assume, r = {(1, 2), (1, 5)}...

Explanation of Solution

c.

Equivalence of expressions:

“Yes”, the expressions will be equivalent if the max is replaced by min...

Explanation of Solution

d.

Proof:

Consider the expression given below:

(r⟖s)⟖t and r⟖(s⟖t)

Assume, r = {(1, 2)}, s = {(2, 3)}, t = {(1, 4)}...

Explanation of Solution

e.

Expression:

Proof:

Consider the expression given below:

σθ(E1⟕E2) and E1⟕σθ(E2)

Let R be of the schema (A, B) and S of (A, C).

Assume, r = {(1, 2)}, s = {(2, 3)} and let u be the expression C = 1...

Expert Solution & Answer

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Check out a sample textbook solution

See solution

Answer 4

Expert Solution & Answer

Chapter 16, Problem 3PE

Explanation of Solution

a.

Proof:

Consider the expression given below:

Π_A(r − s) and Π_A(r)−Π_A(s)

Assume, r = {(1, 2)}, and s = {(1, 3)}...

Explanation of Solution

b.

Proof:

Consider the expression given below:

σ_B<4( _Aγmax(B) as B^(r)) and _Aγmax(B) as B^(σ_B<4^(r))

Assume, r = {(1, 2), (1, 5)}...

Explanation of Solution

c.

Equivalence of expressions:

“Yes”, the expressions will be equivalent if the max is replaced by min...

Explanation of Solution

d.

Proof:

Consider the expression given below:

(r⟖s)⟖t and r⟖(s⟖t)

Assume, r = {(1, 2)}, s = {(2, 3)}, t = {(1, 4)}...

Explanation of Solution

e.

Expression:

Proof:

Consider the expression given below:

σθ(E1⟕E2) and E1⟕σθ(E2)

Let R be of the schema (A, B) and S of (A, C).

Assume, r = {(1, 2)}, s = {(2, 3)} and let u be the expression C = 1...

Expert Solution & Answer

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Check out a sample textbook solution

See solution

Answer 5

Expert Solution & Answer

Answer 6

Expert Solution & Answer

Answer 7

Chapter 16, Problem 3PE

Explanation of Solution

a.

Proof:

Consider the expression given below:

Π_A(r − s) and Π_A(r)−Π_A(s)

Assume, r = {(1, 2)}, and s = {(1, 3)}...

Explanation of Solution

b.

Proof:

Consider the expression given below:

σ_B<4( _Aγmax(B) as B^(r)) and _Aγmax(B) as B^(σ_B<4^(r))

Assume, r = {(1, 2), (1, 5)}...

Explanation of Solution

c.

Equivalence of expressions:

“Yes”, the expressions will be equivalent if the max is replaced by min...

Explanation of Solution

d.

Proof:

Consider the expression given below:

(r⟖s)⟖t and r⟖(s⟖t)

Assume, r = {(1, 2)}, s = {(2, 3)}, t = {(1, 4)}...

Explanation of Solution

e.

Expression:

Proof:

Consider the expression given below:

σθ(E1⟕E2) and E1⟕σθ(E2)

Let R be of the schema (A, B) and S of (A, C).

Assume, r = {(1, 2)}, s = {(2, 3)} and let u be the expression C = 1...

Answer 8

Chapter 16, Problem 3PE

Explanation of Solution

a.

Proof:

Consider the expression given below:

Π_A(r − s) and Π_A(r)−Π_A(s)

Assume, r = {(1, 2)}, and s = {(1, 3)}...

Answer 9

Chapter 16, Problem 3PE

Explanation of Solution

a.

Proof:

Consider the expression given below:

Π_A(r − s) and Π_A(r)−Π_A(s)

Assume, r = {(1, 2)}, and s = {(1, 3)}...

Answer 10

Explanation of Solution

b.

Proof:

Consider the expression given below:

σ_B<4( _Aγmax(B) as B^(r)) and _Aγmax(B) as B^(σ_B<4^(r))

Assume, r = {(1, 2), (1, 5)}...

Answer 11

Explanation of Solution

b.

Proof:

Consider the expression given below:

σ_B<4( _Aγmax(B) as B^(r)) and _Aγmax(B) as B^(σ_B<4^(r))

Assume, r = {(1, 2), (1, 5)}...

Answer 12

Explanation of Solution

c.

Equivalence of expressions:

“Yes”, the expressions will be equivalent if the max is replaced by min...

Answer 13

Explanation of Solution

c.

Equivalence of expressions:

“Yes”, the expressions will be equivalent if the max is replaced by min...

Answer 14

Explanation of Solution

d.

Proof:

Consider the expression given below:

(r⟖s)⟖t and r⟖(s⟖t)

Assume, r = {(1, 2)}, s = {(2, 3)}, t = {(1, 4)}...

Answer 15

Explanation of Solution

d.

Proof:

Consider the expression given below:

(r⟖s)⟖t and r⟖(s⟖t)

Assume, r = {(1, 2)}, s = {(2, 3)}, t = {(1, 4)}...

Answer 16

Explanation of Solution

e.

Expression:

Proof:

Consider the expression given below:

σθ(E1⟕E2) and E1⟕σθ(E2)

Let R be of the schema (A, B) and S of (A, C).

Assume, r = {(1, 2)}, s = {(2, 3)} and let u be the expression C = 1...

Answer 17

Explanation of Solution

e.

Expression:

Proof:

Consider the expression given below:

σθ(E1⟕E2) and E1⟕σθ(E2)

Let R be of the schema (A, B) and S of (A, C).

Assume, r = {(1, 2)}, s = {(2, 3)} and let u be the expression C = 1...

Answer 18

Expert Solution & Answer

Answer 19

Expert Solution & Answer

Answer 20

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Check out a sample textbook solution

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Answer 21

Ch. 16 - Prob. 2PE Ch. 16 - Prob. 3PE Ch. 16 - SQL allows relations with duplicates (Chapter 3),...Ch. 16 - Prob. 5PE Ch. 16 - Prob. 6PE Ch. 16 - Prob. 7PE Ch. 16 - Prob. 8PE Ch. 16 - Prob. 9PE Ch. 16 - Prob. 10PE Ch. 16 - Prob. 12PE

a. Proof: Consider the expression given below: Π A (r − s) and Π A (r)−Π A (s) Assume, r = {(1, 2)}, and s = {(1, 3)}...

Explanation of Solution

a. Proof: Consider the expression given below: ΠA(r − s) and ΠA(r)−ΠA(s) Assume, r = {(1, 2)}, and s = {(1, 3)}...

Explanation of Solution

b. Proof: Consider the expression given below: σB<4( Aγmax(B) as B(r)) and Aγmax(B) as B(σB<4(r)) Assume, r = {(1, 2), (1, 5)}...

Explanation of Solution

c. Equivalence of expressions: “Yes”, the expressions will be equivalent if the max is replaced by min...

Explanation of Solution

d. Proof: Consider the expression given below: (r⟖s)⟖t and r⟖(s⟖t) Assume, r = {(1, 2)}, s = {(2, 3)}, t = {(1, 4)}...

Explanation of Solution

e. Expression: Proof: Consider the expression given below: σθ(E1⟕E2) and E1⟕σθ(E2) Let R be of the schema (A, B) and S of (A, C). Assume, r = {(1, 2)}, s = {(2, 3)} and let u be the expression C = 1...

Want to see the full answer?

Chapter 16 Solutions

a.

Proof:

Consider the expression given below:

Π_A(r − s) and Π_A(r)−Π_A(s)

Assume, r = {(1, 2)}, and s = {(1, 3)}...

b.

Proof:

Consider the expression given below:

σ_B<4( _Aγmax(B) as B^(r)) and _Aγmax(B) as B^(σ_B<4^(r))

Assume, r = {(1, 2), (1, 5)}...

c.

Equivalence of expressions:

“Yes”, the expressions will be equivalent if the max is replaced by min...

d.

Proof:

Consider the expression given below:

(r⟖s)⟖t and r⟖(s⟖t)

Assume, r = {(1, 2)}, s = {(2, 3)}, t = {(1, 4)}...

e.

Expression:

Proof:

Consider the expression given below:

σθ(E1⟕E2) and E1⟕σθ(E2)

Let R be of the schema (A, B) and S of (A, C).

Assume, r = {(1, 2)}, s = {(2, 3)} and let u be the expression C = 1...