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 x = V2. Then x is irrational, and so is 2x = 2V2. Therefore 2x %3D is irrational for any irrational number x. (Note. Find the mistakes in logical reasoning. "Lacks detail" is not a mistake.)

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