$4)$ What is the tax result in the following situations?

a$)$ Taxpayer A purchased her house for $$400,000.$ She put $20\%$ down at the time of the purchase with a $$320,000$ mortgage. The house subsequently decreased in value to $$300,000.$ At that point, Taxpayer A defaulted on the loan. The bank sold the house for $$300,000($non$-$recourse debt$).$ The balance on the mortgage at the time of default was $$290,000($i$.$e$.,$ Taxpayer received $$10,000$ after repayment of the mortgage$).$b$)$ Same as above except Taxpayer A put down $10\%$ and the balance on the mortgage at the time of default was $$330,000($non$-$recourse debt$).$