I have a question regarding the resulting table/relation from a union operation in relational algebra. Does the resulting relation have a primary key? Or does it return a table with a hidden primary key?

Example: Suppose we take the union of the following two tables:

R1:
id | name
----------
1    a
2    b
3    c

R2:
id | name
----------
1    b
2    c
3    d

Where the attribute "id" is primary key in both relation R1 and R2, now the union of those two will be:

id | name
------------
1     a
1     b
2     b
2     c
3     c
3     d

Now none of the attributes in the resulting relation can be primary key since both id and name contain duplicates. How is this resolved by the DBMS?

I have a question regarding the resulting table/relation from a union operation in relational algebra. Does the resulting relation not have a primary key? Or does it return a table with a hidden primary key?

Example: Suppose we take the union of the following two tables:

R1:
id | name
----------
1    a
2    b
3    c

R2:
id | name
----------
1    b
2    c
3    d

Where the attribute "id" is primary key in both relation R1 and R2, now the union of those two will be:

id | name
------------
1     a
1     b
2     b
2     c
3     c
3     d

Now none of the attributes in the resulting relation can be primary key since both id and name contain duplicates. How is this resolved by the DBMS?

i have a question regarding the resulting table/relation from a union operation in relational algebra... Does the resulting relation not have a primery key?, or does it eturn a table with a hidden primary key? Example: Suppose we take the union of the following two tables:

R1:
id | name
----------
1    a
2    b
3    c

R2:
id | name
----------
1    b
2    c
3    d

Where the attribute "id" is primary key in both relation R1 and R2, now the union of those two will be:

id | name
------------
1     a
1     b
2     b
2     c
3     c
3     d

Now none of the attributes in the resulting relation can be primary key since both id and name contain duplicates... How is this resolved by the DBMS? thanks.

I have a question regarding the resulting table/relation from a union operation in relational algebra. Does the resulting relation have a primary key? Or does it return a table with a hidden primary key? 

Example: Suppose we take the union of the following two tables:

R1:
id | name
----------
1    a
2    b
3    c

R2:
id | name
----------
1    b
2    c
3    d

Where the attribute "id" is primary key in both relation R1 and R2, now the union of those two will be:

id | name
------------
1     a
1     b
2     b
2     c
3     c
3     d

Now none of the attributes in the resulting relation can be primary key since both id and name contain duplicates. How is this resolved by the DBMS?