Question

O wor Question 2 5 RQ True False Question 3 5p The union of a countable family of countable sets can be uncountable. True False 5 pt: Question 4

Answer 1

Ques: 2 falpe because R is an uncountable Continum (c) Cardinality and a is set xo Cardinality Cardinalit pet with a Countable Quer: 3 The union seto Can be DnGuntable falpe Proof if A., A₂, ·are Countable Beto let Write A, = {an, ang a, a 23 1 Az {ag, Agz, Agz, ---} An= ? andy and, ens ,

By Contor's dioganalised Counting. a, 912 arz 22 4,3 Qark Gg. Qgg ani and On3 U AA no no Art 9,2 9,3 9e Agro Aps -- } Qoy Aygo good-] AN the elemento the union element and relation with IN ů A is Countable. Hence Proved that union Countable Countable sets Countable. are distinct one - one so "A. nel families of
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