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prove that if all of the 2n subsets of a set containing 2n 1 are equal, then all elements of set n are equal

Sagot :

when multiplicity is removed, you get 2^(2n+1)/2 members, which is 2^(2n).

Take the power set. It has 2^(2n+1) members.

Replace any member which has n+1 or more elements with its complements.

Now the power set has members, which have n or fewer elements, and each such member appears twice.

Therefore, when multiplicity is removed, you get 2^(2n+1)/2 members, which is 2^(2n).

For more information on sets click on the link below:

https://brainly.com/question/2166579

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