Consider the conjecture that the sum of a rational number and an irrational number is ALWAYS irrational. To try to prove this conjecture, Alfred begins with the assumption that the sum is rational. Le

Consider the conjecture that the sum of a rational number and an irrational number is ALWAYS irrational. To try to prove this conjecture, Alfred begins with the assumption that the sum is rational. Let a = a rational number. Let b = an irrational number. Assume a + b = c and c is rational (attempting to disprove the conjecture). a + b = c b = c - a Explain how Alfred's argument contradicts his initial assumption, which proves that the sum cannot be rational.