Which of the following statements regarding traditional IRAs is true?

a$.$ Once a taxpayer reaches $55$ years of age, they are allowed to contribute an additional $$1,000$ a year.

b$.$ Taxpayers with high income are not allowed to contribute to traditional IRAs.

c$.$ Taxpayers who participate in an employer$-$sponsored retirement plan are allowed to deduct contributions to a traditional IRA regardless of their AGI.

d$.$ A single taxpayer with no earned income is not allowed to contribute to a traditional IRA.