Question

write the following expression as a single interval.
$(-\infty,8)\cup(-\infty,11)$

select the correct choice below and, if necessary, fill in the answer box to complete your choice.
\bigcirc a. the single interval that represents $(-\infty,8)\cup(-\infty,11)$ is \boxed{}.
\quad\quad (type your answer in interval notation.)
\bigcirc b. the answer is the empty set.

Explanation:

Step1: Analyze the intervals

The first interval is \((-\infty, 8)\), which includes all real numbers less than 8. The second interval is \((-\infty, 11)\), which includes all real numbers less than 11.

Step2: Find the union

When taking the union of two intervals that both start at \(-\infty\), we look at the right - hand endpoints. Since 8 is less than 11, the union of \((-\infty, 8)\) and \((-\infty, 11)\) will be the interval that includes all numbers from \(-\infty\) up to the larger of the two right - hand endpoints? Wait, no. Actually, \((-\infty, 8)\) is a subset of \((-\infty, 11)\) because every number less than 8 is also less than 11. So the union of a set and its subset is the larger set. So \((-\infty, 8)\cup(-\infty, 11)=(-\infty, 11)\)

Answer:

A. The single interval that represents \((-\infty,8)\cup(-\infty,11)\) is \((-\infty, 11)\)