Louis files as a single taxpayer. In April of this year he received a $$1,020$ refund of state income taxes that he paid last year.

How much of the refund, if any, must Louis include in gross income under the following independent scenarios? Assume the standard deduction last year was $$12,550.$

a$.$ Last year Louis claimed itemized deductions of $$12,920.$ Louis's itemized deductions included state income taxes paid of $$1,870$ and no other state or local taxes.

b$.$ Last year Louis had itemized deductions of $$10,920$ and he chose to claim the standard deduction. Louis's itemized deductions included state income taxes paid of $$1,870$ and no other state or local taxes.

c$.$ Last year Louis claimed itemized deductions of $$14,110.$ Louis's itemized deductions included state income taxes paid of $$2,870$ and no other state or local taxes.