The computer science formalisation of these operations is known as “relational algebra”, which is based on set algebra. That said, the assertion that all eleme

The computer science formalisation of these operations is known as “relational algebra”, which is based on set algebra. That said, the assertion that all elements in a set be equal doesn’t really make sense — or rather, it’d be written as “|S| < 2” by virtue of the fact that a set is defined as containing distinct elements; consequently, in a set with more than one element, all elements are not equal. If you want to use mathematical formalisms for set operations, you’d instead have to work on sets of tuples and test for a predicate: “∀x ∈ S: p(x)”.