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# Multiple choices questions in DBMS, Interview questions in RDBMS, Closure of a set of attributes is a set of attributes, normalization mcq, the closure of a set of attributes is neither a key nor a candidate key

## RDBMS solved MCQ - The closure of a set of attributes is a set of attributes

1. Complete the following sentence with most appropriate of the given options: “The closure of a set of attributes is a set of ________”.

a) keys

b) attributes

c) functional dependencies

d) candidate keys

### The closure of a set of attributes is a set of attributes only.

The closure of a set of attributes A, denoted as A+, is the set of those attributes that can be functionally determined from A. The closure is found to verify whether the set of attributes A can be a candidate key or not.

Let us discuss this statement with an example; consider a relation R(A, B, C, D) with a set of functional dependencies F = {A à B, C à D}. Now, let us find the closure of attribute A. [Refer “how to find closure” for step-by-step explanation]

Steps for finding A+

Result = A     [from trivial FD, A à A]

= AB   [from FD, Aà B]

Result cannot be changed further because neither A nor B nor AB determines any other attributes of R uniquely. So, the result is AB. That is, the closure of A is AB which is a set of attributes from R. Hence, the statement in the question is proved.

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