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A shoe store is running a one-time sale. If you buy a pair of shoes, then you will get another pair of shoes for 50% off.

Dan: “Carolyn does not buy a pair of shoes. Therefore, Carolyn does not get another pair for 50% off.”

Julia: “If Carolyn received a pair of shoes for 50% off, then she bought a second pair.”

If the information in the box is true, whose reasoning is correct?