Claire sells a US Treasury security to the Federal Reserve on the secondary market. She receives a check as payment and then cashes the check at her bank, keeping the cash. Which of the following best describes the result?

a$.$ Both the monetary base and bank reserves will increase.

b$.$ The monetary base will increase, and the Fed will have a new liability.

c$.$ The monetary base will decrease, but bank reserves will stay the same.

d$.$ The monetary base will increase but bank reserves will stay the same.