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.
b. The derivative of any polynomial function is a polynomial function.
c. The sum of the angles of any triangle is 180°.
d. The negative of any irrational number is irrational.
e. The sum of any two even integers is even.
f. The product of any two fractions is a fraction.
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