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Chapter 1: Problem 23

Use graphs to find each set. $$[3, \infty) \cap(6, \infty)$$

Short Answer

Expert verified
The intersection of sets [3, 鈭�) and (6, 鈭�) is (6, 鈭�).

Step by step solution

01

Analyzing each set

The set [3, 鈭�) includes every number greater than or equal to 3. This is marked on the number line with a filled point at 3, indicating 3 is part of the set, extending to the right to show all larger numbers are included. On the other hand, the set (6, 鈭�) includes every number strictly greater than 6, and this is illustrated on the number line with an empty point at 6, representing that 6 itself is not part of the set, and extending to the right to represent all larger numbers.
02

Finding the intersection

The intersection of the sets is the section of the number line where the two sets overlap. In this case, since (6, 鈭�) includes all the numbers greater than 6, but does not include 6 itself, and [3, 鈭�) includes all the numbers greater than or equal to 3, the numbers that are common to both sets are the numbers strictly greater than 6. So, the intersection is (6, 鈭�).
03

Graphical representation

Graphing this on the number line would be as follows: a line drawn extending to the right from the point 6, with an empty point at 6 to indicate that 6 itself is not part of the set. The resulting figure shows that the intersection of [3, 鈭�) and (6, 鈭�) is (6, 鈭�).

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