The statement “The square of any rational number is rational” can be rewritten formally as...

The statement “The square of any rational number is rational” can be rewritten formally as “For all rational numbers x, x2 is rational” or as “For all x, if x is rational then x2 is rational.” Rewrite each of the following statements in the two forms “ _____ x, _____” and “x, if _____, then _____” or in the two forms “ _____ x and y, _____” and “x and y, if _____, then _____.”

a. The reciprocal of any nonzero fraction is a fraction.

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b. The derivative of any polynomial function is a polynomial function.

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c. The sum of the angles of any triangle is 180°.

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d. The negative of any irrational number is irrational.

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e. The sum of any two even integers is even.

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f. The product of any two fractions is a fraction.