Final answer:
The agreement between the host of the castle and Sir Gawain in 'Sir Gawain and the Green Knight' to exchange their daily gains is true, forming a key part of Gawain's test of character. The given statement is true.
Step-by-step explanation:
The statement that the host of the castle makes a deal with Sir Gawain where each man must give the other what he gains from a day's work is true. This is a reference to the medieval romance 'Sir Gawain and the Green Knight', where the host, Lord Bertilak, strikes a bargain with Sir Gawain that for three days, each would exchange with the other what they gained during the day. Gawain is to rest and relax at the castle, while Bertilak goes out hunting. However, this simple agreement becomes a test of Sir Gawain's honesty and chivalry when Bertilak's wife attempts to seduce Gawain.