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!
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(i) Observe that since this means . Now by using the above observation you want to show the implication:
(ii) Same trick.
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