# GATE | Sudo GATE 2020 Mock II (10 January 2019) | Question 36

Consider the following collection of relation schemes:

```professor(profname, deptname)
department(deptname, building)
committee(profname,commname) ```

Find all the professors who are in exactly (i.e., no more and no less) all those committees that Professor Smith is in.
(A)

```R2 <- Πcommname(Πprofname(committee))
R3 <- Πcommname(committee) - R2
(committee / R2) - σprofname = Smith(committee ⋈ R3)```

(B)

```R2 <- Πcommname(Πcommname(committee))
R3 <- σprofname = Smith(committee) - R2
(committee / R2) - Πprofname(committee ⋈ R3)```

(C)

```R2 <- Πcommname(σprofname = Smith(committee))
R3 <- Πcommname(committee) - R2
(committee / R2) - Πprofname(committee ⋈ R3)```

(D) None of the above.

Explanation: Option (C) is correct.

```R2 <- Πcommname(σprofname = Smith(committee))
R3 <- Πcommname(committee) - R2
(committee / R2) - Πprofname(committee ⋈ R3) ```

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