PubTeX output 2020.08.14:1558
3.8 Exercises
1. Prove that:
(a) if and , then .
(b) if and , then .
2. Present a set which contains at least three elements and in which every element is also a subset of the set.
3. Prove or disprove the following: if and , then .
4. Prove that the set of all sets does not exist.
5. Prove that if then .
6. What are the elements of the power set of ? How many elements does this power set have?
7. Let and .
(a) Let and . List all the elements of the set . How many are there?
(b) Prove that .
8. Let be sets. Prove that: and iff
.
9. Prove that:
(a)
(b)
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