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The give set is
contain 5 odd number and 4 even number.
We know that , sum of two integer is even iff both are odd or both are even .
The minimum number n of integer to be selected from ,so that The sum of two of the n integers is even is 2 .
( since , take a set of 2 odd or even integer ).
If the difference of two integer (say ) is 5 then
Therefore the minimum number n of integer selected from S will be 2,so that the difference of two integer is 5.
For example : Take the set .