ok, i think i've got it. the original statement, which i've proven directly, was "if n is odd, then n^2 is odd". so basically a statement in the form p -> q. this is logically equivalent to ~p OR q.
so i can indirectly prove it by showing that ~p OR q is a tautology.
so ~p OR q = "Either n is even or n^2 is odd"
n is even OR n^2 is odd <=>
n = 2k OR n^2 = 2j + 1 <=>
n^2 = 2(2k^2) OR n^2 = 2j + 1 <=>
n^2 is even OR n^2 is odd <=> (which has the form "~q OR q")
T
correct?