Prove that the set of finite binary strings is countable

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Problem 1 - Prove that if A and B are countable sets, then so is A ∪ B

Problem 2 - Prove that the set {0, 1}*, of finite binary strings, is countable.

Problem 3 - For each of the following sets indicate whether it is finite, countably infinite, or uncountable.

1. The set of solution to x³ - x = -0.1

Problem 4 - Describe which of the following sets have bijections between them.

Z R

C Q

P(Z) P(∅)

P(P(∅)) {0, 1}*

{0, 1}^ω {T, F}

P({T, F}) P({0, 1}^ω)

Reference no: EM131690237

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len1690237

10/25/2017 2:40:19 AM

For the Proofs if you guys use bijective, injective, total, function these methods it will be better as these are taught and it will easier for me to understand. For each of the following sets indicate whether it is finite, countably infinite, or uncountable.

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