Homework

Here are some moderately famous lambda terms.

I = ( lambda x . x )

KI = ( lambda y . ( lambda x . x ) )

K = ( lambda x . ( lambda y . x ) )

B = ( lambda x . ( lambda y . ( lambda z . x ( y z ) ) ) )

w = ( lambda x . ( x x ) )

The homework is:
Firstly, for every ordered pair of these famous lambda terms, apply one to the other, and reduce it as far as possible, SHOWING WORK. That's 25 computation tasks. You may use a computer if you wish. You may divide the tasks up among several students operating in a team, if you wish.
Secondly, write a textual explanation of what each of these lambda terms does.