The following post : Prove: $ (A \times C) \setminus (B \times C) = (A \setminus B) \times C $ made me think of the question I am now asking.
Are there frequently used / well known laws for cartesian products in the context of set algebra.
In case such laws exist, can they be proved without analysing the statements in terms of membeship relation ( I mean without using set theory proper)?
Is it possible to " manipulate" cartesian products algebraically and mechanically in the same way one "manipulates" more ordinary sets using DeMorgan's Law, Idempotency Law or Domination law ( for sets) etc. ?