# Math Help - Proof Of Set

1. ## Proof Of Set

For all sets X,Y and Z, prove that if X⊆Y, then
(i) X ∩ Z ⊆ Y ∩ Z
(ii) X ∪ Z ⊆ Y ∪ Z
The problem should be solved in indirect proof way. Thanks!

2. (i) Observe that since $X\subseteq Y$ this means $X = X\cap Y$. Now by using the above observation you want to show the implication:

$x\in X\cap Z \Rightarrow x\in Y\cap Z$

(ii) Same trick.