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Chapter 1: Problem 146

Determine whether each statement makes sense or does not make sense, and explain your reasoning. I prefer interval notation over set-builder notation because it takes less space to write solution sets.

Short Answer

Expert verified
The statement makes sense as interval notation can indeed require less space to write solution sets compared to set-builder notation, particularly for simple linear sets. However, the preference is subjective and depends on the complexity of the solution set.

Step by step solution

01

Understanding Interval and Set-Builder Notation

Firstly, we need to understand what interval and set-builder notations are. Interval notation is a method of writing down a set of numbers. For example, all numbers between \(5\) and \(10\) would be written as \([5, 10]\). Set-builder notation, in contrast, is more comprehensive and descriptive as it might include conditions the members of the set need to fulfill. The same set would be represented as \(\{ x | 5 \leq x \leq 10\}\).
02

Evaluating the Statement

Looking at the given statement, 'I prefer interval notation over set-builder notation because it takes less space to write solution sets.' - it does make sense. Interval notation can indeed be simpler and more concise as it only consists of numbers and basic mathematical symbols, whereas set-builder notation can include complex conditions and occupies more space.
03

Stating the Reasoning

This preference doesn't make the interval notation superior or inferior to set-builder notation; it only means that for simple, linear solution sets, interval notation can be less.space-consuming and simpler to draft.

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