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Let's say we are given this table of the relation Person(name, hobby)

name   hobby
bob    hockey
alice  basketball
mary   cricket
mark   basketball
rick   snowboarding
andy   hockey

How would I use relational algebra to find the hobby that had only one person had.

It should give me

hobby
cricket
snowboarding

My ATTEMPT:

$R1 := \rho_{P2}(Person)$

$R2 := R1 \bowtie_{P2.hobby = P1.hobby \text{ } AND \text{ } P2.name <> P1.name} R2$

$R3 := \pi_{hobby} (R2)$

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  • $\begingroup$ Could you use aggregating functions? $\endgroup$
    – OmG
    Commented Feb 5, 2018 at 23:58
  • $\begingroup$ Just these ----Union ----Intersection ----Difference ----Selection ----Projection ----Cartesian Join ----Theta join ----Natural join $\endgroup$
    – Tinler
    Commented Feb 6, 2018 at 0:02

1 Answer 1

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You need more carefully defined $\theta$-join and then set difference:

$$R1 := \rho_{name1/name,hobby1/hobby}(Person)$$ $$R2 := Person \bowtie_{(hobby=hobby1) \land (name \neq name1)} R1$$ $$R3 := \pi_{hobby}(Person) \setminus \pi_{hobby}(R2)$$

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