Suppose R and S are two relations. The Union operation selects all the tuples that are either in relation R, in relation S, or in both relations R and S. It eliminates duplicate tuples.
For a union operation to be valid, the following conditions must hold:
1. Both relations R and S have the same number of attributes.
2. Corresponding attributes (columns) have the same domain (type).
3. The attributes of R and S must occur in the same order.
4. Duplicate tuples are automatically removed.
⇒ Symbol: ∪
⇒ Notation: R ∪ S
⇒ Relational Algebra: R ∪ S
Suppose R and S are two relations. The Set Intersection operation selects all the tuples that are in both relations R and S.
For a Set Intersection to be valid, the following conditions must hold:
1. Both relations R and S have the same number of attributes.
2. Corresponding attributes (columns) have the same domain (type).
3. The attributes of R and S must occur in the same order.
⇒ Symbol: ∩
⇒ Syntax: R ∩ S
⇒ Relational Algebra: R ∩ S
This version ensures the conditions for compatibility are clear and corrects any grammatical or conceptual errors.
Suppose R and S are two relations. The Set Difference operation selects all the tuples that are present in the first relation R but not in the second relation S.
For a Set Difference to be valid, the following conditions must hold:
1. Both relations R and S have the same number of attributes.
2. Corresponding attributes (columns) have the same domain (type).
3. The attributes of R and S must occur in the same order.
⇒ Symbol: -
⇒ Syntax: R - S
⇒ Relational Algebra: R - S
