Show that A c bar A double bar A bar A SolutionNote closure

Show that A c bar A, double bar A = bar A

Note closure(A) means A bar.

This is a question where we need to prove that closure of a closed set is equal to it.

That is if S is closed closure(S) = S. ------ (1)

And since we know closure of any set A is closed thus closure(A) is closed.

thus using (1)

closure ( closure(A)) = closure(A)

Hence proved,

Another proof:

https://www.proofwiki.org/wiki/Closed_Set_equals_its_Topological_Closure

Example proof:

https://www.khanacademy.org/math/probability/independent-dependent-probability/basic_set_operations/v/subset-strict-subset-and-superset