1. Let \(x\) and \(y\) be rational and irrational numbers, respectively. Is \(x+y\) necessarily an irrational number? Give an example in support of your answer.
\((x + y)\) is an irrational number.
2. Let \(x\) be rational and \(y\) be irrational. Is \(xy\) necessarily irrational? Justify your answer by an example.
, \(xy\) irrational