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

IntroAnalysis

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

dextercioby

It doesn't look right to me. Why would you negate the hypothesis ? This is not reductio ad absurdum.

Let's negate the conclusion: [itex] a\not\subset b [/itex], which means that [itex] \exists x\in a [/itex], so that [itex] x\not\in b [/itex]. But by hypothesis, [itex] \forall x\not\in b, x\not\in a [/itex]. Contradiction, right ?

IntroAnalysis

You are correct. I see the difference. Thank you for the help.