Below is a proof showing that the sum of a rational number and an irrational number is an irrational number.

It is the sum of two rational numbers

Step-by-step explanation:

Given that a is a rational number and b is an irrational number.

To prove that a+b is irrational.

Here contrapositive method is used to prove

If possible assume a+b is rational and equal to x

Then we have

a+b = x

b = x-a = x+(-a)

On right side we have sum of two rational numbers hence right side is rational.

But left side b is irrational thus a contradiction

{3 + i, 3 - i, 3, -1}

step-by-step explanation: