Problem 146 - College Algebra Essentials

Question

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.

Step-by-Step Solution

Answer

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 1: 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 \(\{ x | 5 \leq x \leq 10\}\).

Step 2: 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.

Step 3: 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.