Taxpayers, a married couple, filed a joint return in Year $1$ and received a state income tax refund of $$5,000$ in Year $2.$ To what extent is the $$5,000$ refund included in their gross income in Year $2$ in the following circumstances if in Year $1$:

A$)$ Taxpayers claimed the standard deduction in computing their taxable income?

B$)$ Taxpayers had $$20,000$ of the total state property and income taxes and $$20,000$ of other itemized deductions?

C$)$ Taxpayers had $$12,000$ of total state property and income taxes and $$20,000$ of other itemized deductions?

D$)$ Taxpayers had $$13,000$ of total state property and income taxes and $$15,000$ of other itemized deductions?