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