Problem 126 of 7
Prove rational/irrational closure statement irrational minus rational is irrational.
Using a hint is okay. It just tells the trainer to give you a little more review.
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use definitions and contradiction reasoning.
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Statement must be a true closure or nonclosure theorem with stated conditions.
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Your answer is equivalent to the expected form.
Walkthrough
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1. Translate rational numbers into fraction form or assume contrary for irrational statement.
2. Use algebraic operations preserving rationality.
3. Reach the desired rational form or contradiction.
Use the worked steps, then substitute the final answer back into the original relationship to confirm it satisfies the prompt.
Proof by examples only when a general proof is requested.