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Problem 30

Show that the complement of the complement of a set is the set itself.

Expert verified

To show that the complement of the complement of a set is the set itself, we need to prove that for any set A, (A')' = A. Since the complement of a set A, denoted as A', contains all elements not in A, and the complement of A', denoted as (A')', contains all elements not in A', we must show that for any element x, x is in (A')' if and only if x is in A. By proving both directions, we establish that (A')' = A, confirming that the complement of the complement of a set is the set itself.

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