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 proving that the sum cannot be rational

a) if c is rational, either b or a would have to be rational as well.
b) if a is rational, either b or c would have to be rational as well.
c) if b is irrational, the difference of two rational numbers could never be equal to it.
d) if a + b is rational, then a and a could be either rational or irrational.