Gate 2004 doubt on foreign keys

Question

 

Referencing to this gate ques- https://gateoverflow.in/16095/gate2004_13-let-and-two-relation-schema-where-the-primary-key

Let R1 (A, B, C) and R2 (D, E) be two relation schema, where the primary keys are shown underlined, and let C be a foreign key in R1 referring to R2. Suppose there is no violation of the above referential integrity constraint in the corresponding relation instances r1 and r2. 

how does projection _C (r₁) - projection _D (r₂)  we will get empty relation?

For referential integrity to hold in a relational database, any column in a base table that is declared a foreign key can contain either a null value, or only values from a parent table's primary key or a candidate key. 

So C can  have null or duplicate values in foreign key, subtracting entities of D from C can still have null and other values(those were duplicate). So, how will it get empty set?

 

Comments

Projection removes the duplicates right?

Also, why will we consider null as an element in the projection? If any element is NULL in C then we don't need to bother about it..

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if C has NULL in it then the query projection _C (r₁) - projection _D (r₂) will be a set containing null which isn't empty set . Hence the answer would be wrong.

 

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@MiNiPanda