The sum of rational numbers may be rational or irrational

  1. A number r is said to be rational if there exist integers a and b such that r = a/b. An integer is a “counting number” such as 1, 2, 3, 4 and so on, or 0, or the negative of a counting number. Prove or disprove the following statements. You may assume that √ 2 is irrational.

(a) The sum of rational numbers may be rational or irrational.

(b) The sum of two irrational numbers is irrational.

(c) The sum of a rational number and an irrational number is irrational also.

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