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GATE DA 2025 Q17: Relational algebra on Car, Make and Own

Question

Consider the following three relations:

Car(model,year,serial‾,color)\texttt{Car}(\texttt{model}, \texttt{year}, \underline{\texttt{serial}}, \texttt{color})

Make(maker,model‾)\texttt{Make}(\texttt{maker}, \underline{\texttt{model}})

Own(owner‾,serial‾)\texttt{Own}(\underline{\texttt{owner}}, \underline{\texttt{serial}})

A tuple in Car represents a specific car of a given model, made in a given year, with a serial number and a color. A tuple in Make specifies that a maker company makes cars of a certain model. A tuple in Own specifies that an owner owns the car with a given serial number. Keys are underlined; (owner, serial) together form key for Own. (⋈\bowtie denotes natural join)

πowner(Own⋈(σcolor=“red”(Car⋈(σmaker=“ABC” Make))))\pi_{\texttt{owner}}\big(\texttt{Own} \bowtie (\sigma_{\texttt{color}=\text{“red”}}(\texttt{Car} \bowtie (\sigma_{\texttt{maker}=\text{“ABC”}}\,\texttt{Make})))\big)

Which one of the following options describes what the above expression computes?

Try it: multiple choice: exactly one correct option

Select one option
Wrong answer costs 1/3 mark in GATE.
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Answer: C (official GATE 2025 final answer key)

Concept used: Reading selection, natural join and projection from the inside out.

First step: Start with the innermost part: σmaker=“ABC”Make\sigma_{\texttt{maker}=\text{“ABC”}}\texttt{Make} keeps only ABC's models, and joining with Car keeps only cars of those models.

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Source: official GATE 2025 DA question paper and final answer key, organised by IIT Roorkee. Question paper · Answer key

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