In $2023,$ Bogdan loses his job when his employer closes. Because Bogdan is struggling to pay his monthly expenses, he arranges a decrease in his

mortgage from $$160,000$ to $$120,000$ with his mortgage lender. His basis in the home is $$200,000$ and the fair market value at the time of the

mortgage reduction is $$250,000.$ Bogdan also has $$10,000$ of student loan debt forgiven in $2023$ under a federal program to forgive students loans for

lower$-$income individuals.

What amount of the cancellation of debt must Bogdan include in his income in $2023?$

What is Bogdan's basis in his home after applying exclusion provisions $($if any$)?$