Union Compatibility and Important relations

Union compatibility:-

Two relations(tables) are said be union compatible if:-

  • Both have the same number of attributes (columns)
  • Corresponding attributes are of the same type.
  • Duplicate tuples should be automatically removed.

let suppose there are two relations or tables R and S and 

\left | R \right |=m  .......// Cardinality of R means the number of rows or tuples  in R

\left | S \right |=n

then the number of tuples is given by this

Operation Minimum Maximum
Product        \left | R* S \right | mn mn
Join               \left | R\bowtie S \right | 0 mn
Left join       \left |R  ⟕ S| m mn
Right Join  |R  ⟖ S| n mn
Full Join     |R ⟗ S| (m+n )or  max(m,n) mn

Example:-

Consider the join of a relation R with a relation S. If R has m tuples and S has n tuples then the maximum and minimum sizes of the join respectively are:-

Solution:

maximum size means  all the common attribute value in R is mapped with each value of the common attribute in S, So total is mn

for minimum: nothing is matched. So 0

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