Final answer:
The set of elements in (-∞,8) or (-∞,16) or in both is (-∞,16), representing the union of these intervals.
Step-by-step explanation:
The set of elements in (∞,8) or (∞,16) or in both sets represents all the real numbers that are less than 16. This is because the set of numbers less than 8 (∞,8) is fully contained within the set of numbers less than 16 (∞,16). Therefore, the union of these two intervals does not extend beyond the larger interval.
To visualize this concept, you can think of the number line where the interval (∞,8) is a segment that starts from negative infinity and ends right before 8. Since (∞,16) is also a segment that starts from negative infinity, but it extends further to end right before 16, it includes all elements of the first interval and adds more up to 16. Thus the combination of both, whether considering their intersection or union, is simply the interval (∞,16).
The term that describes the combination of these intervals is the union.