Let k = 0 + 5. A) Show the union of k countable sets is countable....

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Let k = 0 + 5. A) Show the union of k countable sets is countable....

Let k = 0 + 5.
A) Show the union of k countable sets is countable.

any help will be useful

engineering Computer-Science

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Answer 1

Answer #1

Proof. Let two sets A={an:n∈N} and B={bm:m∈N}. Then we can define a new sequence c, such that, the first n elements in c are n elements of A and next m elements are elements of B, and then duplicates are

So , and p<= m+n.

Hence for any 2 sets, of length n,m which are countable, their union, A U B is also countable.

C1 U C2 is countable,

Let C1 U C2 U... U C(k-1) is also countable, then by induction, we can say that C1 U C2 U ... Ck is also countable.

Thinking logically, if we can count number of elements in 2 or more finitte different sets, then we can also count the number of elements of their unions.

I hope it helps. For any doubt, feel free to ask in comments, and give upvote if u get the answer.

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Answer 2

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Let k = 0 + 5. A) Show the union of k countable sets is countable....

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Let k = 0 + 5. A) Show the union of k countable sets is countable....

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