contacted a mechanics shop to have them inspect my air conditioning on my corvette, since it stopped working this summer. The shop told me to bring it to their shop at $8$:$00$am on August $26,2020,$ and that the inspection would cost $$75.$ I agreed, but unfortunately, I forgot to bring it into the shop. The mechanics shop contacted me and stated that I owed them $$75,$ since they did not have any other car to work on at $8$:$00$am on August $26,2020.$ Since they did not do any work for me$,$ I do not want to pay them.

Question $13$ options:

I do not need to pay them, since they did not do the work.

I do not need to pay them, since it was not in writing.

I do need to pay them, since I offered them the gift of $$75.$

I do need to pay them, since we had a contract, and I breached.

None of these