Sorry, I posted a similar question earlier, but I kind of messed it up. So here's the correct one.
Q: If B is a proper subset of C, then C - B does not equal the empty set. Is this statement always true, always false, or sometimes true and sometimes false? Explain.
I get that if B is a proper subset of C, then there must be at least one element within the set C that doesn't belong in set B. And for C - B to take place, I explained that x must be a member of C and can't be a member of B. But I really don't know how to tie these relations together. Am I getting hot or cold?
More precisely, for x ∈ C - B to take place, x must be a member of C and can't be a member of B. Also, C - B does not equal the empty set iff there exists an x ∈ C - B. Taken together, C - B does not equal the empty set iff there exists an x such that x is a member of C and not a member of B. Now compare this with