It’s been called to my attention that there is a typo on the key I gave out for Homework 2. A new version will be posted online shortly, but the changes are few, so you might just pencil it into your copy. Addition: The error goes back a bit further than I originally thought, the problem arose because I didn’t substitute the value of [17]^M properly into [18]^M.

The last couple of lines of the evaluation of (3) (“Loren is cute or it is not the case that Pavarotti is hungry”) are missing a ¬, and should read:

[18]^M = {x: <x, [17]^M> ∈ [14]^M }

= {x: <x, (TRUE iff ¬[PAVAROTTI is hungry in M]) > ∈ {<TRUE,FALSE>, <FALSE,TRUE>, <TRUE,TRUE>}}

= {TRUE} iff PAVAROTTI is hungry in M, and {TRUE, FALSE} otherwise.

[19]^M = TRUE iff [11]^M ∈ [18]^M

= TRUE iff (TRUE iff LOREN is cute in M) ∈ ({TRUE} iff PAVAROTTI is hungry in M, and {TRUE, FALSE} otherwise)

= TRUE iff (LOREN is cute in M) ∨ ¬(PAVAROTTI is hungry in M)

Incidentally, there’s no real difference between Pavarotti and PAVAROTTI—both refer to the individual Pavarotti. I changed my typographical convention relatively arbitrarily, but the point is mainly just to call attention to the fact that the word “Pavarotti” is different from the individual PAVAROTTI.