4. Explain what is wrong in the following "proof." CLAIM. Let x be a real number. If a is irrational, then 2x is irrational. "PROOF." Take r = V2. Then r is irrational, and so is 2x = 2/2. Therefore 2x is irrational for any irrational number c. (Note. Find the mistakes in logical reasoning. "Lacks detail" is not a mistake.) 5. Give a complete proof by contradiction of the claim in item 4. (Recall. A number is rational iff it can be written as the quotient of two integers.)