Textbook Question
Use the rules for radicals to perform the indicated operations. Assume all variable expressions represent positive real numbers. √11 • √44
1
views
Ch. R - Review of Basic Concepts
Lial13th EditionCollege AlgebraISBN: 9780136881063
Not the one you use?Change textbookSelect a different textbook
Table of contents
Chapter 1, Problem 49
Determine whether each statement is true or false. {x | x is a natural number less than 3}= {1, 2}
Verified step by step guidance1
Understand the set notation: {x | x is a natural number less than 3} means the set of all natural numbers x such that x is less than 3.
Recall the definition of natural numbers: natural numbers are typically the positive integers starting from 1, i.e., {1, 2, 3, 4, ...}.
Identify all natural numbers less than 3: these are 1 and 2, since both are natural numbers and both are less than 3.
Write the set explicitly: {x | x is a natural number less than 3} = {1, 2}.
Compare this with the given set {1, 2} and conclude that the statement is true because both sets contain exactly the same elements.
Verified video answer for a similar problem:
This video solution was recommended by our tutors as helpful for the problem above.
Video duration:
1mWas this helpful?
Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Set Notation
Set notation is a way to describe a collection of elements using curly braces {}. The vertical bar '|' means 'such that,' and it specifies a condition that elements must satisfy to be included in the set. For example, {x | x is a natural number less than 3} describes all natural numbers x that are less than 3.
Recommended video:
05:18
Interval Notation
Natural Numbers
Natural numbers are the set of positive integers starting from 1, 2, 3, and so on. They do not include zero or negative numbers. Understanding what counts as a natural number is essential when interpreting sets defined by conditions involving natural numbers.
Recommended video:
2:51The Natural Log
Set Equality
Two sets are equal if and only if they contain exactly the same elements. Order and repetition do not matter in sets. To determine if {x | x is a natural number less than 3} equals {1, 2}, we check if both sets have the same elements without any extras.
Recommended video:
05:18Interval Notation
Related Practice
Textbook Question
Find each product. (5r-3t2)2
2
views
Textbook Question
Simplify each expression. Write answers without negative exponents. Assume all variables represent nonzero real numbers. 48/46
Textbook Question
Find each sum or difference. -2 - |-4|
Textbook Question
Multiply or divide, as indicated. ac + ad + bc + bd/a2 - b2 * a3 - b3/2a2 + 2ab + 2b2
Textbook Question
Factor each trinomial, if possible. See Examples 3 and 4.
5
views