Suppose I have 100 lists, each list contains many sets. For example,
L1 = [{2,7},{2,7,8},{2,3,6,7},{1,2,4,5,7}]
L2 = [{3,6},{1,3,4,6,7},{2,3,5,6,8}]
L3 = [{2,5,7,8},{1,2,3,5,7,8}, {2,4,5,6,7,8}]
....
L100=[{},{},{}]
I need to find intersections between each set of L1, L2, L3, ...L100, i.e., $Intersect(L) = \lbrace\bigcap e | e \in \lbrace L1,...,L100 \rbrace \rbrace $
Now, if I partition these 100 lists into smaller groups, e.g., 3 groups (number of lists in each group may be different, but 1 list just belongs to 1 group)
- Group 1: From L1 to L33
- Group 2: From L34 to L66
- Group 3: From L67 to L100
Then, I calculate
$Intersect(L1) = \lbrace\bigcap e | e \in \lbrace L1,...L33 \rbrace \rbrace$
$Intersect(L2) = \lbrace\bigcap e | e \in \lbrace L34,...L66 \rbrace \rbrace$
$Intersect(L3) = \lbrace\bigcap e | e \in \lbrace L67,...L100 \rbrace \rbrace$
I want to ask that the following is true?
$Intersect(L) = \lbrace\bigcap e | e \in \lbrace Intersect(L1), Intersect(L2), Intersect(L3) \rbrace \rbrace $
Thank you very much.