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Because the entropy lost by the reaction goes to the surroundings, and the surroundings are gaining the entropy, this means that the entropy gained by the surroundings is equal to that lost by the reaction. If the entropy for the reaction decreased by 1 J/K (-1 J/K), for example, then the entropy of the surroundings would increase by 1 J/K (+1 J/K). This fulfills the equation deltaS(total)=deltaS(surroundings)+deltaS(system).
Keep in mind that the second law is referring to the total entropy, aka the entropy of the universe. So, the entropy of the system or of the surroundings can increase without violating the second law as long as the total entropy is not negative.
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