$.$ In each of the following independent situations, determine the amount of the charitable contribution and the limitation that would apply. If multiple answers exist, determine all of them. In each case assume the contribution is given to a public charity.

a$)$ Jack purchases a historical document for $$50,000.$ He donates the historical document to a public charity $2$ years later. The public charity plans to use it immediately. Its FMV at the time of the donation is $$100,000.$

b$)$ Valerie donates vintage clothing to a public charity. The clothing was purchased for $$500$ and its FMV at the time of the donations was $$1,200.$ She purchased the clothing $7$ months ago.