prove whether the set property is true, false, or sometimes true and sometimes false?
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?
Re: prove whether the set property is true, false, or sometimes true and sometimes fa
Quote:
Originally Posted by
Taurus3 
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.
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.
That is all correct.
Re: prove whether the set property is true, false, or sometimes true and sometimes fa
wait, but how do tie all these together? :( Like is this always true?
Re: prove whether the set property is true, false, or sometimes true and sometimes fa
Quote:
Originally Posted by
Taurus3 wait, but how do tie all these together? :( Like is this always true?
Tie what together?
The statement that B is a proper subset of C means
Re: prove whether the set property is true, false, or sometimes true and sometimes fa
It does not mean that 
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Re: prove whether the set property is true, false, or sometimes true and sometimes fa
wait, then can I still conclude that this is always true by the 1st and 3rd statement?
Re: prove whether the set property is true, false, or sometimes true and sometimes fa
Quote:
Originally Posted by
emakarov It does not mean that
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That depends upon whom you ask.
I have seen it defined both ways.
Re: prove whether the set property is true, false, or sometimes true and sometimes fa
Quote:
Originally Posted by
Taurus3 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.
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
Quote:
Originally Posted by
Taurus3 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.
