5 More Countability Given: ·A is a countable, non-empty set. For all i E A, Si i

Question

5 More Countability Given: ·A is a countable, non-empty set. For all i E A, Si is an uncountable set. . B is an uncountable set. For all i e B, Qi is a countable set. For each of the following, decide if the expression is "Always Countable", "Always Uncountable" "Sometimes Countable, Sometimes Uncountable" For the "Always" cases, prove your claim. For the "Sometimes" case, provide two examples - on where the expression is countable, and one where the expression is uncountable. (a) AnB (b) AUB (c) UieA Si (d) ieA S (e) UieB Qi (f) nieB Qi

Explanation / Answer

here

1)A interjuction B .it is a countable because we write a common of A and B here a is countable the maximum length of set a is length of the set A

2) A union B it is a uncountable set because here B is a uncountable and length of th set is also a uncountable

3) here it is also be uncountable because here S is a uncountable and length of th set is also a uncountable

4)it is a countable because we write a common of S and A here a is countable the maximum length of set a is length of the set A

5)it is uncountable because here Q is a uncountable and length of th set is also a uncountable

6)it is countable because we write a common of Q and B here Q is countable the maximum length of set a is length of the set Q

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