I need to define some operators with properties like idempotence and distribution over union and intersection so that *Mathematica* can symbolically simplify expressions. How do I define such operators?

For example, I want to define $⋃$ and $⋂$ such that 

$\qquad (A ⋂ B) ⋃ B = B$

for all $A$ and $B$ and, whenever $A ⊂ B$, then 

$\qquad A ⋂ B = A {\rm \ and\ } A⋃ B = B$