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

Question 2 we know that set of rational numbers ij Countable and set of Real number Ý uncountable 2) Colinality (@) # Gudinality (R) =) R&Q ie set of reals not equevialent to set of retinals. So Answer is false

Question_3- let A,,A₂,... are countable sets. have to becove that U An Ý Countable. nal 1912 1913 1914 دی Roof let us weite A.- {aui A2 = {azı {a21 1922 1923, 924 {431,282, 2331 - 3 Az 1 بما An= { ani, anzi 3 here aij stands for the jth element of the ith set- let us define height of the set as height of ay = itj with this definition height of an ey and an is the only element of height 2 Simularly, the height of air and an ý 3 and these are the only elements of height

So similar observation can be made about the elements of height m, these are (ml) in number and these are alimt, a2,m.2, a3 n-3 arrange these elements elements according to their height au , 212,921, a 13,922 asi these elements cover all elements of u An I. An ý Countable. nal - ) Answer = False
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