Proof Help: Prove (A∪B)-C ⊆ A∪(B-C)

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SUMMARY

The proof that (A∪B)-C ⊆ A∪(B-C) is established by taking an arbitrary element x from the set (A∪B)-C. The proof involves demonstrating that if x is in (A∪B)-C, then x must either belong to A or B, while not being in C. By analyzing both cases—when x is in A and when x is in B—it is shown that x must also belong to the set A∪(B-C), confirming the subset relationship.

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Ja6464
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I am stuck on a proof question:

Prove (A∪B)-C ⊆ A∪(B-C)

If anyone would be able to help me with this proof it would be much appreciated, as I have an exam on this topic tomorrow afternoon!

Thanks a lot.
 
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In a proof like this (checking if a set is included into another) you typically take one arbitrary element x from the first set, and prove that it also belongs to the second set. (So any element from the first is included in the second, so the first set is a subset of the second.)

If x is in the first set, then it is either in A or in B (or both), but certainly not in C. Try to figure out each of the two cases (x in A, x in B), and see if, in both cases, x belongs to the second set.

Hope this helps.
 
Thank you that's helped a lot, I think I've managed to prove it now.

Hopefully I can do it again tomorrow!
 

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