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Chapter 0: Problem 24

Use graphs to find each set. $$[2, \infty) \cap(4, \infty)$$

Short Answer

Expert verified
The intersection of the sets [2, \(\infty)\) and (4,\(\infty)\) is the set (4, \(\infty)\).

Step by step solution

01

Plot the Intervals

Start by drawing a number line. For the first set, [2, \(\infty) \), draw a closed circle at 2 to indicate that 2 is included in the set, and then draw a line going off to the right to indicate that the set goes on to infinity. For the second set, (4, \(\infty)\), do the same, but this time draw an open circle at 4 to indicate that 4 is not included in the set, and then draw a line going off to the right.
02

Find the Intersection

The intersection of two sets is the set of all elements that are in both sets. On the number line, this corresponds to the part where both the lines for the two sets overlap. In this case, the two lines start overlapping from the point 4 onwards. So the intersection of the two sets is the set (4,\(\infty)\). Note that the intersection begins at 4, but does not include 4 because the second set didn't include 4.

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