Let x, y, z, a, b, c be the attributes of an entity set E. If {x}, {x,y},…
2014
Let x, y, z, a, b, c be the attributes of an entity set E. If {x}, {x,y}, {a,b}, {a,b,c}, {x,y,z} are superkeys then which of the following are the candidate keys?
- A.
{x,y} and {a,b}
- B.
{x} and {a,b}
- C.
{x,y,z} and {a,b,c}
- D.
{z} and {c}
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Correct answer: B
A candidate key is a minimal superkey, meaning no proper subset of it is also a superkey.
Given the superkeys: {x}, {x,y}, {a,b}, {a,b,c}, {x,y,z}.
{x} is a superkey of size 1, so it has no proper subsets to check. It is minimal.
{x,y} contains {x}, which is a superkey, so it is not minimal.
{a,b} is a superkey, and neither {a} nor {b} are listed as superkeys, making it minimal.
{a,b,c} contains {a,b}, so it is not minimal.
{x,y,z} contains {x}, so it is not minimal.
Thus, the candidate keys are {x} and {a,b}.
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