If A, B, and C are sets, prove: (A - B) is a subset of C iff (A - C) is a subset of B.
I've already wasted hours on this problem (I hardly know where to start), so I would appreciate any help. Thank you!
2006-10-09 05:35:59 · 4 answers · asked by Anonymous in Science & Mathematics ➔ Mathematics
First part: prove that if (A-B) is a subset of C, (A-C) is a subset of B.
Assume that x is (A-C), but not in B. That means x is in A, but not in either B or C.
Then, x is in (A-B). But (A-B) is a subset of C, so x is in C, which contradicts our earlier statement that x is not in C.
Therefore, the assumption that x is not in B is wrong, so (A-C) must be a subset of B.
Part 2: prove that if (A-C) is a subset of B, then (A-B) is a subset of C.
This part can be done in the same way as the first part.
2006-10-09 05:45:49 · answer #1 · answered by James L 5 · 1⤊ 0⤋
let A={1,2,3},B={2) and C={1,3}
here (A-B)={1,3}
subsetr of C
(A-C))={2} subset of B
proceed along these lines
2006-10-09 05:55:30 · answer #2 · answered by raj 7 · 0⤊ 1⤋
What theorem is this? I don't think it is true as written.
2006-10-09 05:55:34 · answer #3 · answered by bequalming 5 · 0⤊ 0⤋
have you tried drowning them in Venn shapes ???
i would have drown it to you but you cant do that here sorry
try to do it and i will try to see how i can sen it to you
are you supposed to it by Venn shapes by the way ?
2006-10-09 05:49:07 · answer #4 · answered by Anonymous · 0⤊ 2⤋