Question

Prove the union of two countable sets is countable.

Answer 1

Hey MATE!

Lema 1. The union of two countable sets is countable.

Proof. Let A={an: n∈N} and B={bn: n∈N}. Then we can define the sequence (cn)∞n=0 by
c2k=ak and c2k+1=bk.

For every k∈N. Now A∪B={cn:n∈N} and since it is a infinite set then it is countable.

By Lemma 1 you can prove your proposition by induction on the number of sets of the family

Corollary. The union of a finite family of countable sets is a countable set.

Hope it helps

Hakuna Matata :))

Answer 2

HII DEAR❤❤❤❤❤❤

Prove the union of two countable sets is countable.》》》》

The union of two countable sets is countable. Proof. Let A and B becountable sets and list their elements in finite or infinite lists A = {a1,a2,...}, B = {b1,b2,...}. ... Of course, if both A and B are finite we will end up with a finite list of the elements of A ∪ B.

HOPE IT HELPS YOU....!!