Set theory question it , thank you

AI Thread Summary
The discussion revolves around a set theory homework question involving two statements about sets A, B, and C. The first statement, A⊆B if and only if B'⊆A', is argued to be false based on Venn diagram analysis, while the second statement, if A∩C ⊆ B∩C then A⊆B, is believed to be true. The user expresses urgency and stress due to multiple homework questions due soon. They seek clarification and assistance with their reasoning and proofs for these statements. The conversation highlights the challenges of understanding set theory concepts and the importance of visual aids like Venn diagrams in problem-solving.
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set theory question please help it urgent, thank you

Homework Statement



1. Homework Statement

Let A, B and C be any sets inside our universal set U. Decide whether each of the following statements is true or false. Justify your answers by giving a proof or a counterexample as appropriate.

a) A⊆B if and only if B'⊆A'

b) If A∩C ⊆ B∩C then A⊆B

2. Homework Equations

X \ Y sets of elements in X but not Y. Y doesn't have to be a subset of X however if it is then X \ Y is the compliment of Y in X

3. The Attempt at a Solution

this is how i did it however i don't think its right hence i need your help thanks

a) with these 2 venn diagrams it shows that this statement is false as the elements don't have to be in set A or B , please see the attatched file for the diagrams , I am not sure please help thank you

b) With this venn diagram i think it shows the statement is true, this is as the set A has the the same elements that are also in set B therefore the statement is true. please help me out on this , see the attached document (i named the doc 2A for the first part n 2B for the second) thank you, please help
Attached Files



Homework Equations





The Attempt at a Solution

 
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Nothing is attached.
 


Nevermind...didn't see the other thread.
 


thanks for the help, I am soo stressed with this and i got 6 other questions which I am still working on, I've done 9 and this is in for monday, please help, thanks
 

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