set differenceif r1 and r2 are two union

Question

Set Difference

If R1 and R2 are two union compatible relations or relations then result of R3 =R1- R2 is the relation that have only those tuples that are in R1 but not in R2.

Incase, R3 will have tuples such that R3 = {t | R1 ∋ t ∧ t∉R2}.

 

Example:

 

R1

 

X Y A1 B1 A7 B7 A2 B2 A4 B4

 

  R2  

A	B
A1	B1
A2	B2
A3	B3
A4	B4
R1-R2 =

 

R1-R2 =

A	B
A3	B3
R2-R1=

 

R2-R1=

A	B
A7	B7

Note: -1) Difference operation is not commutative, i.e.,

 R1 - R2 ≠ R2 - R1

2) Difference operation is not associative, i. e.,

R1 - (R2 - R3) ≠ (R1 - R2) - R3