(Section 3.2, problems 12, 14) Section 01 does not need to answer this question. Section ZG81 answers this question.

12. Statement: The product of any irrational number and any rational number is irrational.

Proposed negation: The product of any irrational number and any rational number is rational.

14. Statement: For all real numbers x 12 = x 2 2 t h e n x 1 = x 2 .

Proposed negation: For all real numbers x 12 = x 2 2 t h e n x 1 = x 2 .

x1 and x1 and x2 , if x2, if