There's a lot of laws that have same ideas in Logic operations and operations of set. (Examples : I.$((P∧Q)∨R) = ((P∨R)∧(Q∨R))$ and $((A∩B)∪C) = (A\cup C)\cap(B\cup C)$,II.De Morgan's Laws.etc) Hence I want to ask that What's the relation among Boolean Algebra,propositional logic,and set theory? Are they some kind of equivalent?
And finally, Do Boolean Algebra, propositional logic, and set theory share the same laws of operation? (If they do, were there anyone proved that they do, or they don't?) >>>>BTW,Does that mean all these laws I proved with Truth Table in Logic can be used in Set theory??