In 2006, Joe and Jane, a married couple, borrowed $600,000 from a local bank and purchased a home worth $1 million. After the Great Recession, though, the fair market value of that home fell to $500,000 and they found that they could no longer afford the mortgage payments. In 2010, they and the bank reached an agreement whereby the bank would discharge $300,000 of debt. Will Joe and Jane be treated as having realized $300,000 for tax purposes? Why or why not?