SOLUTION: My Question is: Let X = {1,2,...,n}, A = {A⊆X | n ∉ A} and B = {A⊆ X | n ∈ A}. Show that |A|=|B| by (BP). (I understand what each set means where A is the set where n is

Question 1164827: My Question is: Let X = {1,2,...,n}, A = {A⊆X | n ∉ A} and B = {A⊆ X | n ∈ A}. Show that |A|=|B| by (BP).
(I understand what each set means where A is the set where n is not included and B is the set where n is included, I believe I am only counting the subsets of each set and not the elements in each set but im not sure how to do that exactly)
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!

What you wrote is "Show that the cardinality of set A is equal to the cardinality of set B", that is the number of elements in A is equal to the number of elements in B, which is not true. Set B has n elements and Set A has n - 1 elements. You cannot prove that the number of subsets of A is equal to the number of subsets of B, because that is not a true statement either.

There are twice as many subsets in B as in A because the number of subsets in A is

and the number of subsets in B is

and

John

My calculator said it, I believe it, that settles it

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