91Ó°ÊÓ

The intersection of two sets includes all the elements that are common to both sets. Think of it like finding the overlap between two groups. For example, if Set A is \([-8, -2]\) and Set B is \([-10, -3]\), their intersection would be the numbers they both share. When dealing with intervals, the intersection will be another interval that falls within the overlapping range.

In our exercise, Set 1 is \( (-\infty,-6] \) and Set 2 is \([-9, \infty)\). To find the intersection, we look for numbers that are in both sets. This involves finding the overlap of the ranges these intervals cover.

Visualizing sets on a number line can greatly help in understanding their intersection. A number line is a straight horizontal line that shows numbers in increasing order from left to right. To visualize Set 1, you can draw an arrow starting from \(-\infty\) and ending at -6, coloring the point at -6 to indicate it is included. For Set 2, draw an arrow starting at -9 going towards \(\infty\), marking the -9 point to show it is included.

By examining the visualization, we can easily spot the overlapping part. In this case, it is the interval between -9 and -6, with both boundaries included because they share these elements. This visualization helps us to write the intersection clearly as \([-9, -6]\).

Inclusive intervals are denoted by square brackets \([ ]\), meaning that the endpoints are part of the set. In our exercise solution, the endpoints -9 and -6 are included in the intersection of the sets. When writing intervals inclusively, always use square brackets to show that the boundary values are part of the set.

For example, in \([-9, -6]\), -9 and -6 are part of the interval, meaning any number between and including -9 and -6 is contained in both sets. Always pay attention to the brackets used in interval notation, as this tells you whether the endpoints are included \([ ]\) or excluded \(( )\).