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I have a problem in identifying the key constraints of the Entity set. 
 

As in the relation, the key constraint should be from M-side. 

But here, in this case, according to me Father is the key constraint.
So for this, the relation is 1:M. In this case, it doesn't satisfy Father to be the key constraint.

2 Answers

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HERE Father is not key as in relation of relationship (has)

as

father son

f1       a1

f1       a2

f2       b1

f2       b2

as attribute father not uniquely determine relation (has)

but son attribute uniquely determine relation
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There are some properties that you should keep in mind:

1. a key attribute should be unique, it should not repeat itself. FOr eg, an aadhar no. is unique as it identifies a particular person

           father           son

            f1                 a1

             f1                 a2

             f2                b1

             f2                 b2

this is wrong for f1, f2 to be key attributes as f1, f2 are repeating.

2. an attribute cannot be multivalued, for eg.  

            father            son

              f1                 a1, a2

             f2                 b1, b2

this is wrong.

conclusion: there is no way in which you can write write f1, f2 once and uniquely identify their children without making it multivalued.

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