Final answer:
The set of elements common to both intervals ∞,14) and ∞,19) is ∞,14), which represents the intersection of these intervals from negative infinity up to, but not including, 14.
Step-by-step explanation:
The set of elements common to both intervals ∞,14) and ∞,19) is ∞,14). This is because the elements that are common to both sets are all the numbers that are less than 14, which are also included in the numbers that are less than 19. This overlap of two intervals is known as their intersection. Visually, if you imagine the real number line, this intersection includes all points from negative infinity up to, but not including, 14.
This concept is essential in understanding how to combine sets to find a common subset, which is fundamental in set theory and calculus. To denote this mathematically, we would write the intersection of the two intervals as (-∞, 14) ∩ (-∞, 19) = (-∞, 14).