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Topology: Homework
MAT246: Concepts in Abstract Math
August 2024
Reminder
This problem set is due on Tuesday August 13th. You will need to upload your solutions to Gradescope. The problems will be graded for both correctness and clarity of the proof!
Problem 1. Given two recursively enumerable sets X and Y show that there exist two non-intersecting recursively enumerable sets X' c X and Y' c Y such that X' U Y' = X U Y.
Problem 2. Describe a Turing machine with alphabet 0, 1 that duplicates the given input. For example if the input is ”011” after the machine enters its final state the tape should read ”011011” .