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

  • #1
IntroAnalysis
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Homework Statement





Homework Equations





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.

Homework Statement





Homework Equations





The Attempt at a Solution

 

Answers and Replies

  • #2
dextercioby
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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 ?
 
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  • #3
IntroAnalysis
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You are correct. I see the difference. Thank you for the help.
 

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