Proof by contrapositive
I am having a terrible time understanding this one:
Prove that for all x E r, and y E R, if x is rational and y is irrational, then x + y is irrational. use proof by contradiction known as contrapositive.
OK I understand that contrapositive (~p --> ~q) so
Proof: if x is not rational then y is not irrational
Now I have no idea what to do next?
Please help, I have a test coming up in two days and I need to grasp this stuff.(Headbang)
So assume the negation of the conclusion.
Originally Posted by robasc
Original conclusion: x + y is irrational
Negation of it: x + y is rational
So under this assumption you can write x + y = r, where r is in Q (rationals). Now what happens when you solve for y?
I have no idea, I am assuming that the answer will be false because a rational number and a irrational number will conclude to be an irrational number but how do I prove that?