7
2
4
5
3

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Mathematica code

`Select[Subsets[Range@12,{6}],!Or@@(IntegerQ[#2/#]&@@#&/@Subsets[#,{2}])&]`

returns all the $S$ sets

`{4, 5, 6, 7, 9, 11}, {4, 6, 7, 9, 10, 11}, {5, 6, 7, 8, 9, 11}, {5, 7, 8, 9, 11, 12}, {6, 7, 8, 9, 10, 11}, {7, 8, 9, 10, 11, 12}`

So the answer is $4$