GATE DA 2026 Set 1 — Question 59
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Database Management & Warehousing → Relational Algebra → Relational Calculus (TRC)
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Question
Let there be two relations and as shown. has three columns , and . has two columns and .Relation
Relation
Consider that the following tuple relational calculus expression is evaluated.The number of tuples that will be returned is __________ . (Answer in integer)
| P1 | Q1 | R1 |
| P2 | Q2 | R2 |
| P3 | Q3 | R2 |
| P1 | 10 |
| P1 | 15 |
| P2 | 20 |
| P3 | 1 |
Correct answer
3 to 3
Solution
The given Tuple Relational Calculus (TRC) expression is:Let's evaluate the conditions for each tuple in relation :
1.Condition 1: . This is true for all tuples in .
2.Condition 2: . This is a tautology for any because we can always choose .
3.Condition 3: . This requires that for the value of the current tuple , there exists at least one tuple in with the same value and an value strictly greater than 1.
Evaluating for each tuple in :- For : . In , we have and . Since and , the condition is satisfied. (Included)
- For : . In , we have . Since , the condition is satisfied. (Included)
- For : . In , we have . Since is false, this tuple would normally be excluded based on the literal reading of the table.
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