Pierre, a cash basis, unmarried taxpayer, had $$3,170$ of state income tax withheld during $2023.$ Also in $2023,$ Pierre paid $$793$ that was due

when he filed his $2022$ state income tax return and made estimated payments of $$2,219$ towards his $2023$ state income tax liability. When

Pierre files his $2023$ Federal income tax return in April $2024,$ he elects to itemize deductions, which amount to $$14,550,$ including the state

income tax payments and withholdings, all of which reduce his taxable income.

a$.$ What is Pierre's $2023$ state income tax deduction?

$

b$.$ As a result of overpaying his $2023$ state income tax, Pierre receives a refund of $$1,268$ early in $2024.$ The standard deduction for single

taxpayers for $2023$ was $$13,850.$ How much of the $$1,268$ will Pierre include in his $2024$ gross income?