/*! 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 30 Determine whether \(\subseteq, \... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 2: Problem 30

Determine whether \(\subseteq, \subset\), both, or neither can be placed in each blank to form a true statement. $$ A=\\{x \mid x \in \mathbf{N} \text { and } 3

Short Answer

Expert verified
The correct statement is: \(A \subset B\). This signifies that A is a proper subset of B.

Step by step solution

01

Understanding the sets

First, identify what elements the sets A and B consist of. According to the definitions, set A contains natural numbers greater than 3 and less than 10, that is - numbers 4, 5, 6, 7, 8, 9; and set B contains natural numbers between 2 and 16, that is - numbers 2, 3, 4, 5, ....15, 16.
02

Comparing the sets

Now, compare set A and set B. It's clear that all elements in set A are also in set B, but set B contains additional elements.
03

Identifying the relationship between the sets

The elements of set A are entirely contained within set B, but set A is not equal to set B, because set B contains additional elements. Thereby, set A is a 'proper subset' of set B and not just a 'subset'. The correct symbol to use between A and B, therefore, is '\(\subset\)'.

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!

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

In Exercises 41-66, let $$ \begin{aligned} U &=\\{\mathrm{a}, \mathrm{b}, \mathrm{c}, \mathrm{d}, \mathrm{e}, \mathrm{f}, \mathrm{g}, \mathrm{h}\\} \\ A &=\\{\mathrm{a}, \mathrm{g}, \mathrm{h}\\} \\ B &=\\{\mathrm{b}, \mathrm{g}, \mathrm{h}\\} \\ C &=\\{\mathrm{b}, \mathrm{c}, \mathrm{d}, \mathrm{e}, \mathrm{f}\\} \end{aligned} $$ Find each of the following sets. \(B \cup U\)

In Exercises 41-66, let $$ \begin{aligned} U &=\\{\mathrm{a}, \mathrm{b}, \mathrm{c}, \mathrm{d}, \mathrm{e}, \mathrm{f}, \mathrm{g}, \mathrm{h}\\} \\ A &=\\{\mathrm{a}, \mathrm{g}, \mathrm{h}\\} \\ B &=\\{\mathrm{b}, \mathrm{g}, \mathrm{h}\\} \\ C &=\\{\mathrm{b}, \mathrm{c}, \mathrm{d}, \mathrm{e}, \mathrm{f}\\} \end{aligned} $$ Find each of the following sets. \(B \cup C\)

Let $$ \begin{aligned} U &=\\{\mathrm{a}, \mathrm{b}, \mathrm{c}, \mathrm{d}, \mathrm{e}, \mathrm{f}, \mathrm{g}, \mathrm{h}\\} \\ A &=\\{\mathrm{a}, \mathrm{g}, \mathrm{h}\\} \\ B &=\\{\mathrm{b}, \mathrm{g}, \mathrm{h}\\} \\ C &=\\{\mathrm{b}, \mathrm{c}, \mathrm{d}, \mathrm{e}, \mathrm{f}\\} \end{aligned} $$ Find each of the following sets. \((A \cup B)^{\prime} \cap C\)

Let $$ \begin{aligned} U &=\\{1,2,3,4,5,6,7\\} \\ A &=\\{1,3,5,7\\} \\ B &=\\{1,2,3\\} \\ C &=\\{2,3,4,5,6\\} \end{aligned} $$ Find each of the following sets. \(\left(C^{\prime} \cap A\right) \cup\left(C^{\prime} \cap B^{\prime}\right)\)

Determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. \(A \cap A^{\prime}=\varnothing\)
See all solutions

Recommended explanations on Math Textbooks

Probability and Statistics

Read Explanation

Calculus

Read Explanation

Pure Maths

Read Explanation

Mechanics Maths

Read Explanation

Discrete Mathematics

Read Explanation

Applied Mathematics

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.