Set theory question it , thank you

[dhillon]

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

 

[gb7nash]

Nothing is attached.

 

[gb7nash]

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

 

[dhillon]

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