Questions about sets and subsets.

[shle]

Hi, the question goes as follows:

Given two subsets X and Y of a universal set U, prove that: (refer to picture)

I'm having particular trouble on D and E, if anyone can clear this up or provide some clarification for me that would be appreciated! I know a venn diagram might not be possible here so just an explanation is ok

Thank you!

 

[pka]

Hi, the question goes as follows:
Given two subsets X and Y of a universal set U, prove that: (refer to picture)
I'm having particular trouble on D and E

For part D, note that "If X then Y" is exactly the same as "If not Y then not X".

E. \(\displaystyle X\cup(Y\setminus X)=X\cup(Y\cap X^c)=X\cup Y=~?.\)