What is proof$-$of$-$work?

a requirement to define an expensive computer calculation, also called mining, that needs to be performed in order to create a new group of trustless transactions $($blocks$)$ on the distributed ledger or blockchain

a way to validate transactions and achieve a distributed consensus

a type of digital currency in which a record of transactions is maintained and new units of currency are generated by the computational solution of mathematical problems; it operates independently of a central bank

All of the answers are correct.