Step 1: Recall what the foreign key constraint requires.
E is a foreign key in S that references A, the primary key of R. This means every value of E that appears in relation s must also appear as a value of A in relation r. The constraint is checked on the value stored in S, against the values available in R.
Step 2: Check option (A), inserting into r.
Inserting a new record into r only adds new possible values of A. It does not remove or change any value of A that existing rows in s might be referencing, so it can never break the constraint. This operation is always safe.
Step 3: Check option (B), deleting from s.
Deleting a record from s only removes a row, it does not add a new E value that would need to match an A value in r. Since removing rows from the referencing relation cannot create a broken reference, this operation is always safe.
Step 4: Check option (C), deleting from r.
If a deleted row from r had an A value that some row in s references through E, that reference would now point to nothing, breaking the constraint. So this operation can violate the constraint, depending on the data. It is not always safe.
Step 5: Check option (D), inserting into s.
A new row inserted into s might have an E value that does not exist as any A value in r. That would break the constraint immediately. So this operation can also violate the constraint. It is not always safe.
Final Answer:
Only inserting into r (A) and deleting from s (B) can never violate the foreign key constraint.
\[ \boxed{\text{(A) and (B)}} \]