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.

The assumption that c is rational means that the difference c-a must be rational. That difference is b, so b=c-a would mean that b must be rational. But b is defined to be irrational. Since an irrational number cannot equal a rational number, a contradiction arises and the assumption that c is rational must be false. Therefore the sum (c) must be irrational. (B)

amayaoliver amayaoliver · Answer 2 · 2019-03-07T00:32:29+01:00

amayaoliver amayaoliver

07-03-2019

Answer:

Remember that b = c - a. If b is irrational, the difference of two rational numbers could never be equal to it

Answer Link