(b) Theorem: Q is a countable set. 1 Proof: Let Ao {0}, and let An= {; = 3 n Each A is countable, for k = 0, 1, 2..... W

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B Theorem Q Is A Countable Set 1 Proof Let Ao 0 And Let An 3 N Each A Is Countable For K 0 1 2 W 1 (14.75 KiB) Viewed 37 times

(b) Theorem: Q is a countable set. 1 Proof: Let Ao {0}, and let An= {; = 3 n Each A is countable, for k = 0, 1, 2..... We have Q = Ak. km0 Therefore Q is a countable set. (i) Explain why (2) is true. (ii) Explain why (3) is true. (iii) Why does (3) prove the theorem? 12 n n 2 n ....} for ne N. (1) (2) (3) [12 marks]