Consider the following three relations in a relational database. Employee(eId, Name), Brand(bId, bName), Own(eId, bId) Which of the following relational algebra expressions return the set of eIds who own all the brands?

_eId(_eId, bId(Own) / _bId(Brand))

_eId(Own) - _eId≤ft((_eId(Own) × _bId(Brand)) - _eId, bId(Own))

_eId(_eId, bId(Own) / _bId(Brand))

_eId(Own) - _eId≤ft((_eId(Own) × _bId(Brand)) - _eId, bId(Own))

_eId(_eId, bId(Own) / _bId(Own))

_eId≤ft((_eId(Own) × _bId(Own)) / _bId(Brand))

GATE CSE 2022 Q25: Relational algebra for employees who own all brands

Consider the following three relations in a relational database.

$Employee(\underline{eId}, Name)$ , $Brand(\underline{bId}, bName)$ , $Own(\underline{eId}, \underline{bId})$

Which of the following relational algebra expressions return the set of $eId$ s who own all the brands?

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Answer: A, B (official GATE 2022 final answer key)

Concept used: "Owns all brands" is relational division by the set of all brand ids, which can also be written with product and difference.

First step: Check what each divisor is: all brands (from $Brand$ ) or only the brands someone owns (from $Own$ ).

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Source: official GATE 2022 CS question paper and final answer key, organised by IIT Kharagpur. Question paper · Answer key