Question: Discrete Structures comp sci Problem 1. (10 points) Recall that a set A is countably infinite when there is a bijection from the set N

Discrete Structures

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Discrete Structures comp sci Problem 1. (10 points) Recall that a set

Problem 1. (10 points) Recall that a set A is countably infinite when there is a bijection from the set N to A. Prove each of the following statements: a. b. C. d. If A, B are countably infinite then so is AU B. Every infinite subset of a countably infinite set is countably infinite. If A, B are countably infinite then so is A B. The set Qof rational numbers is countable. (Hint: represent each rational number as a subset of Z (N-(0), making sure that no rational number is represented twice in your subset)

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