## How many tuples would result in a natural join operation / The number of records that a natural join produce in relational algebra

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**Question:**

**9. Assume a relation R(A, B, C) with n tuples(records) and a relation S(C, D) with m tuples. Let us suppose that the Natural Join (⋈) between R and S (ie., R ⋈ S) produces t tuples as the result. Which of the following (n, m, t) number of tuples is TRUE for this natural join?**

(a) (6, 12, 720)

(b) (1, 1, 3)

(c) (10, 5, 2)

(d) (10, 5, 100)

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**Answer:**

**(c) (10, 5, 2)**

*Natural Join (⋈) between R and S can result in maximum of nXm number of records if n and m are the number of tuples in R and S respectively.*

**This is the maximum limit. It can never exceed this.**Natural join matches the value of common attributes of both tuples. If there is a match, then result will include that tuple. If no match that tuple will be discarded. Hence, a natural join may results in minimum zero and maximum nXm records. The result (10, 5, 2) may be true if we have 10 records in R and 5 records in S and only two tuples matches the join condition.
For (6, 12, 720), 720 > 6 * 12. Hence, it is impossible.
For (1, 1, 3), 3 > 1 * 1. Hence, it is impossible.
For (10, 5, 100), 100 > 10 * 5. Hence, it is impossible.

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