Example set-cover implementation in GNU MathProg. Pick the minimal set of sentences which contain all the characters. Run with `glpsol --math setcover.mod --output /dev/fd/0`

setcover.mod

set Sentences;
set Characters;

param contains{s in Sentences, c in Characters};

var chosen{s in Sentences} binary;

minimize size: sum{s in Sentences} chosen[s];

s.t. all_characters_covered{c in Characters}: sum{s in Sentences} contains[s, c] * chosen[s] >= 1;

data;

set Sentences := 1 2 3 4 5;
set Characters := 1 2 3 4 5 6 7 8 9;
param contains default 0
        : 1 2 3 4 5 6 7 8 9 :=
        1 1 1 1 0 0 0 0 0 0
        2 0 0 1 1 0 1 0 1 1
        3 1 0 1 0 1 0 1 0 1
        4 1 1 1 1 1 0 0 0 0
        5 0 0 0 1 0 0 1 1 1;

end;