GATE CSE 2000 | Question: 2.25

Question

Given relations r(w, x) and s(y, z) the result of

select distinct w, x 
from r, s 

is guaranteed to be same as r, provided.

• A. r has no duplicates and s is non-empty
• B. r and s have no duplicates
• C. s has no duplicates and r is non-empty
• D. r and s have the same number of tuples

Comments

in given question result always different tuple  show in relation r has no duplicate this is the key point of the question

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Detailed Video Solution, with Variations & Complete Analysis: https://youtu.be/zb6vXpZVo1E?t=2122&feature=shared

Variation 1:

If "distinct" keyword is not there in the question, & $s \neq \phi$ then "$r \subseteq output$"

Variation 2:

If "distinct" keyword is not there in the question, then answer will be: "Either $R = \phi$ or $|S| = 1$."

Watch Above Video Solution for Complete Analysis. 

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@Deepak Poonia Variation 3:

If "distinct" keyword is not there in the question, then ans will be r=phi && |s|=anything

Answer 1

This question is about SQL, in SQL Relations are MULTISET, not SET. So, $R$ or $S$ can have duplicated.

Answer: A.

A. If $R$ has duplicates, in that case, due to distinct keyword those duplicates will be eliminated in final result. So, $R$ can not have duplicates. If $S$ is empty $RXS$ becomes empty, so $S$ must be non empty. This is true.

B. Here, assume that S is empty. (No duplicates.) Then R X S will be empty. SO this is false.

C. Same argument as B.

D. Assume that $R$ has duplicates. Then Distinct keyword will remove duplicates. So, result of query $!= R$, so This is false.

Comments

yes

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Hello to all

What if in place of option a) statement, this is written "R is empty"

Then also correct option is a)

Am I correct?

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Doesn’t the Definition of Candidate Key itself disallow 2 Tuples to Be Same?

I mean if a Relation Has No Proper Subset of Attributes as  Candidate Key, it will have All attributes combined as Candidate Key and so , 2 tuples can’t be same i guess.

Answer 2

(a)

if s is empty r x s will give empty set, so s cant be empty

Comments

@Arjun Suresh: Agree with you. r has no duplicates doesn't make sense here.

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@Arjun, This questions is about SQL. In SQL we allow relations to have duplicates. Check my answer here !

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yes In SQL, relation can have duplicate tuples

Relation

A	B
1	2
4	9
1	2

the above relation, it is valid in SQL but not in Relational Algebra.

Answer 3

 

Option A would have been correct if the only condition was on S that S should be non empty

Even if R has duplicates, it will exexute correctly

 

 

1. S is empty
   1. 
2. S is non empty
   1. 

Answer 4

r has no duplicate and s is not empty then rXs will  will be non empty and using select distinct w,x  we will gwt r as r has no dublicate

so here we have to think about 2 important things

first is s should not be empty as then rXs will be empty

second is r should not contain duplicate as in ans we are using distinct keyword!!

so option a is correct.

Answer 5

l