If R1 and R2 are two union compatible relations or functions, then the result of R3 = R1 ∩R2 is the relation that contains all tuples that are in both the relations In other words, R3will have tuples such that R3 = {t | R1 ∋ t ∧ R2 ∋ t}.
Example:
R1
A
B
A1
B1
A2
B2
A3
B3
A4
B4
R2
A7
B7
X
Y
R3 = R1 ∩ R2 is
Note: 1) Intersection is an associative operation, i.e., R1 ∩ (R2 ∩ R3) = (R1 ∩ R2) ∩ R3
2) Intersection is a commutative operation, i.e., R1 ∩ R2 = R2 ∩ R1