# Questions about sets and subsets

#### shle

##### New member
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!​

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#### CaptainBlack

##### Well-known member
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