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

  • #1

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
Science Advisor
Homework Helper
Insights Author
13,019
568
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 ?
 
Last edited:
  • #3
You are correct. I see the difference. Thank you for the help.
 

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

Replies
5
Views
17K
Replies
2
Views
2K
  • Last Post
Replies
3
Views
1K
  • Last Post
Replies
11
Views
5K
Replies
11
Views
986
Replies
18
Views
2K
Replies
3
Views
25K
Top