The printed version of Hwk2 contains a trivial typo with bad consequences:

In the last line of problem 14, a comma is missing after the phrase

  , where N = { square, star, triangle}

before 

    is a subring.

That's crucial, because I mean to say P(N) is a subring (of P(M)). 
N is of course a subset of M, not a subring;  without the comma, 
the sentence would be incomplete anyways...

In the online version, I've fixed it already.