1
Union, intersection, and minus (set difference) require the two relations to be union compatible.
2
Union compatibility means two relations must have the same degree (same number of attributes) and the same attribute domains.
3
Union operation (R U S) includes all tuples from R, S, or both, while eliminating duplicate tuples.
4
Intersection operation (R ∩ S) includes only the tuples that exist in both R and S, eliminating duplicates.
5
Minus operation (R - S) includes tuples that are present in R but not in S. Order matters (R - S is different from S - R).
6
Cartesian product (R x S) combines every tuple from the left relation with every tuple from the right relation and does not require union compatibility.
7
For a Cartesian product, if relation R has degree P and relation S has degree N, the resulting degree is P + N. If cardinalities are C1 and C2, the resulting cardinality is C1 * C2.