In Problem 2.6.4 (b), are the ⊂ symbols meant to denote "strict subset", so that the sets can't be equal? You didn't define that symbol.
Those two occurrences of ⊂ are mistakes -- they each should be the ordinary subset symbol ⊆. That symbol is usually used to mean "strict subset" as you say, but I haven't used it at all in the book. In fact in this example if you interpret them as strict subset the given statement is not always true.
Last modified 20 September 2007