Final answer:
Carol's recognized loss on the sale of a gifted dining room table is $0 because losses on personal use property are generally not deductible for tax purposes.
Step-by-step explanation:
Carol's recognized loss on the sale of the gifted table is indeed $0. This is true because when determining a loss on property received as a gift, the basis for loss is the giver's adjusted basis at the time of the gift, which is $3,200 in this case. Since Carol sold the table for $2,000, which is less than Jan's adjusted basis, a loss could be recognized.
However, for tax purposes, losses on personal use property like furniture are generally not deductible, so Carol's recognized loss would be $0.