Why is a set union operation independent in relational algebra? Why it cannot by expressed by the other four basic operations (selection, projection, cartesian product and difference)? What kind of queries require set union?
The other operations you list all have the property that they cannot map two values appearing in different columns of their input relations into the same column. Clearly this property is preserved by function composition. But UNION does allow mapping values into the same column, so it cannot be constucted by compositions of the other operations.