# Thread: 2 simple proof questions, logic related

1. ## 2 simple proof questions, logic related

1.Suppose x and y are real numbers. Prove or give a counterexample.

if x + y is irrational, the x is irrational or y is irrational.

I found a counterexample already in a earlier question that asked if x is irrational and y is irrational, then x + y is irrational, but im not sure how to approach this question.

2.If x is a real number, then $\displaystyle |x-2| \leq 3$ implies that$\displaystyle -1 \leq x \leq 5.$

for this one, im not sure how to deal with the absolute value.
Thanks

2. For the second one, take an alternative definition of absolute value,

|x|=$\displaystyle \sqrt{x^2}$ then the equation is easily solved as long as you remember to take both positive and negative square root when the time comes

3. prove the first one by proving the contrapostive and use the fact that the sum of two rational numbers is a rational number (easiest to see if you use fractions and remember that all the variables are integers)