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Chapter 2: Problem 50

Express each set in the simplest interval form. $$ (5,11] \cap[6, \infty) $$

Short Answer

Expert verified
[6, 11]

Step by step solution

01

- Identify the Sets

First, identify the given sets. The sets are \((5,11]\) and \([6, \infty)\).
02

- Understand Intersection

The operation to perform is intersection, denoted by \(\cap\). The intersection of two sets contains elements that are common to both sets.
03

- Find the Intersection

Identify the common elements in both sets. For the sets \((5,11]\) and \([6, \infty)\), the common elements start from 6 (since 6 is in both sets) and go up to 11 (since 11 is the upper bound in the first set).
04

- Write in Interval Notation

Combine the common elements in the simplest interval form. The intersection of \((5, 11]\) and \([6, \infty)\) is \([6, 11]\).

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

set intersection
The intersection of two sets is a fundamental concept in set theory. It's symbolized by \(\backslashcap\), which means

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