/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 17 Find each indicated intersection... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 4: Problem 17

Find each indicated intersection or union. $$ \\{2,4,16\\} \cap\\{4,16,256\\} $$

Short Answer

Expert verified
\(\{4,16\}\)

Step by step solution

01

Understand the Intersection Operation

The intersection of two sets results in a new set containing only the elements that are common to both original sets.
02

List Elements of Both Sets

First, list the elements of each set. The first set is \(\{2,4,16\}\) and the second set is \(\{4,16,256\}\).
03

Identify Common Elements

Next, identify which elements are present in both sets. The elements common to both \(\{2,4,16\}\) and \(\{4,16,256\}\) are 4 and 16.
04

Form the Intersection Set

Create a new set containing the common elements found in the previous step. Thus, the intersection of \(\{2,4,16\}\) and \(\{4,16,256\}\) is \(\{4,16\}\).

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

Key Concepts

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

Intersection Operation
The intersection operation is a basic concept in set theory. When we talk about the intersection of sets, we mean finding the elements that are shared between these sets.
Imagine you have two groups of friends, and you want to know who belongs to both groups. This is similar to finding the intersection of sets.
In mathematical terms, if we have two sets, say Set A and Set B, the intersection is denoted as \(A \cap B\). The result is a set containing elements that are present in both Set A and Set B. For example, in our exercise, the intersection of \(\{2,4,16\}\) and \(\{4,16,256\}\) results in a new set containing the common elements 4 and 16.
Common Elements
Finding common elements is a key part of performing the intersection operation. Let's break this down step by step:
First, list all the elements in each of the sets. For our example, we have:
  • First set: \(\{2,4,16\}\)
  • Second set: \(\{4,16,256\}\)
Now, look for elements that are present in both lists. Here, we see that 4 and 16 are present in both sets.
Common elements are the backbone of intersection; without shared elements, the intersection would be empty. In essence, you are looking for the overlap or the 'common ground' between the sets.
This technique is extremely useful not only in mathematics but also in everyday problem-solving.
Set Theory
Set theory is the foundation upon which much of modern mathematics is built. It deals with collections of objects called sets. Sets are denoted by curly braces, { }, and they can contain numbers, letters, or even other sets.
One of the fundamental operations in set theory is the intersection, which we have covered. Other basic operations include union, difference, and complement.
  • Union: The union of two sets is a new set containing all the elements from both sets.
  • Difference: The difference of two sets is a new set containing the elements present in one set but not the other.
  • Complement: The complement of a set contains all the elements not in the set, relative to a universal set.
Set theory is not just limited to numbers; it can be applied to various fields including computer science, logic, and statistics. Understanding the basics of set theory can help you tackle more complex problems in these areas.

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

The function given by $$ F(d)=(4.95 / d-4.50) \times 100 $$ can be used to estimate the body fat percentage \(F(d)\) of a person with an average body density \(d\) in kilograms per liter. A woman's body fat percentage is considered healthy if \(25 \leq F(d) \leq 31 .\) What body densities are considered healthy for a woman?

Age of Marriage. The following rule of thumb for determining an appropriate difference in age between a bride and a groom appears in many Internet blogs: The younger spouse's age should be at least seven more than half the age of the older spouse. Let \(b=\) the age of the bride, in years, and \(g=\) the age of the groom, in years. Write and graph a system of inequalities that represents all combinations of ages that follow this rule of thumb. Should a minimum or maximum age for marriage exist? How would the graph of the system of inequalities change with such a requirement?

Graduate-School Admissions. Students entering a master's degree program at the University of Louisiana at Lafayette must meet minimum score requirements on the Graduate Records Examination (GRE). The GRE Verbal score must be at least 145 and the sum of the GRE Quantitative and Verbal scores must be at least \(287 .\) Each score has a maximum of \(170 .\) Using \(q\) for the quantitative score and \(v\) for the verbal score, write and graph a system of inequalities that represents all combinations that meet the requirements for entrance into the program.

Solve and graph. Write the answer using both set-builder notation and interval notation. $$ |t-7|+3 \geq 4 $$

Write an equivalent inequality using absolute value. $$ -5 \leq y \leq 5 $$
See all solutions

Recommended explanations on Math Textbooks

Probability and Statistics

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Calculus

Read Explanation

Logic and Functions

Read Explanation

Decision Maths

Read Explanation

Mechanics Maths

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.