The type of verbal is participle and the verbal phrase is “playing the piano”
The complete infinitive phrase in this sentence is 'to learn methods for solving equations', because 'to learn' is the infinitive, but the rest of the phrase also has to be included.
It means the way the writer uses the language to convey meanings, feelings e.t.c. In another context it may mean the way the writer uses language in order to manipulate the reader and lead him where he/she desires e.g. to feel in a certain way about a character, to have certain expectations e.t.c.
The correct answer is b.The close relationship between sumo wrestlers could be an incentive
for an elite wrestler to throw a match he doesn’t need to win.
If people all know each other, there are various reasons why one could lose a match on purpose for his friend.