MHB 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!​

 

[CaptainBlack]

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!​

d) Show that \( X\subseteq Y\) implies \(\overline{Y} \subseteq \overline{X}\)

Other than the Venn diagram where the region representing \(X\) is inside that representin \(Y\) so that the coplement of \(Y\) is contained within the complement of \(X\) (You are strongly recomended to draw the diagram), Consider any \(z \not\in Y\), then it is in \(\overline{Y}\), but because \( X\subseteq Y\) it is also not in \(X\), so is in \(\overline{X}\), which proves the result.

CB