26. Exemplar Exercise Problems IV

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.

 

NoYes $(x + y)$ is necessarilynot necessarily an irrational number.

 

2. Let $x$ be rational and $y$ be irrational. Is $xy$ necessarily irrational? Justify your answer by an example.

NoYes, $xy$ necessarilynot necessarily irrational