Closure in $<P([0,1)),\{\bigcup, \bigcap\}> $

Question

I need to define the closre of the sub set $M:=\{[a,b):0\leq a\leq b<1\}$ in the algebra $<P([0,1)),\{\bigcup, \bigcap\}>$.

Where do I start? I can think only of specific examples to elements that belong or not belong to $Cl(M)$ but I don't know how to generalize my specific examples.

Answer 1

I've managed to prove that $Cl(M) = \{\emptyset\}\cup \{[a'_1,a''_1)\cup ... \cup [a'_n, a''_n) : n\in \omega, 0\leq a_1'< a_1''< a'_2<...< a_n''<1\} $ by proving that each set is a subset of the other set.