Question

Given two relations R₁(A, B) and R₂(C, D), the result of following query

Select distinct A, B

from R₁, R₂

is guaranteed to be same as R₁ provided one of the following condition is satisfied.

1. R₁ has no duplicates and R₂ is empty.
2. R1 has no duplicates and R2 is non-empty.
3. Both R₁ and R₂ have no duplicates. 
4. R₂ has no duplicates and R₁ is non - empty

Answer 1

Correct Answer - Option 1 : R₁ has no duplicates and R₂ is empty.

CONCEPT:

• SQL Relations are MULTISET, not SET. So, R₁ or R2 can have duplicated.
• If S is empty, then R₁ × R₂ = empty and hence it will not equal R
• If R₁ has duplicates, in that case, due to distinct keywords those duplicates will be eliminated in the final result and SQL query will not be equal to R₁. So, R₁ cannot have duplicates.

EXPLANATION:

Option 1: R₁ has no duplicates and R₂ is non-empty

This is true:

Option 2: R and S has same number of tuples

Since R1 can be duplicate it is false

Option 3: R₁ and R2 have no duplicates

Since S can be empty ∴ R × S = 0 it is false

Option 4: R2 has no duplicates and R1 is non-empty

Since R can be duplicate it is false

Example:

R₁(x, y)

A	B
1	2
1	2

 

R₂(A, B)

y	z
3	4
5	2

 

R1 × R2:

A	B	C	D
1	2	3	4
1	2	5	2
1	2	3	4
1	2	5	2

 

SELECT DISTINCT w, x from R, S

Output:

w	x
1	2

 

This proves option 2, 3 and 4 an incorrect statement