## Could someone check this proof?! If c\b subset c\a, then prove a subset b

1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution
Assume c\b is a subset of c\a. This means if x Є c Λ (Not Є) b, then it is an Є c Λ (Not Є) a.

Assume x Є c Λ (Not Є) b, but is Not Є c Λ (Not Є) a. Then x Є c Λ a. But this contradicts,
c\b is a subset of c\a. Therefore, a must be subset of b.
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

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 Blog Entries: 9 Recognitions: Homework Help Science Advisor It doesn't look right to me. Why would you negate the hypothesis ? This is not reductio ad absurdum. Let's negate the conclusion: $a\not\subset b$, which means that $\exists x\in a$, so that $x\not\in b$. But by hypothesis, $\forall x\not\in b, x\not\in a$. Contradiction, right ?
 You are correct. I see the difference. Thank you for the help.