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Chapter 1: Problem 1

Indicate whether the given statement is true or false. $$3 \in\\{1,3,5,8\\}$$

Short Answer

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Step by step solution

01

Understand the Meaning of the Symbols

The symbol \( \in \) is used to denote that an element belongs to a set. So, we need to determine if the number 3 is an element of the set \( \{1, 3, 5, 8\} \).
02

Identify the Elements of the Set

The set provided is \( \{1, 3, 5, 8\} \). The elements of this set are 1, 3, 5, and 8.
03

Check for the Element in the Set

Look at the elements of the set and see if the number 3 is listed among them. Since 3 is indeed one of the elements, it belongs to the set.
04

Make the Conclusion

Since we found the number 3 within the set \( \{1, 3, 5, 8\} \), the statement is true.

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Key Concepts

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

set theory
Set theory is a fundamental theory in mathematics that studies sets, which are essentially collections of objects. These objects can be numbers, symbols, or even other sets. Understanding sets is critical for various areas of mathematics. For example, if we have a set of numbers \({1, 2, 3, 4}\), these numbers are called the elements of the set. Sets can be finite or infinite and are denoted by curly braces, e.g., \({a, b, c}\). In set theory, we use various operations to describe relations between sets, such as union, intersection, and difference. Learn the basics of sets to enhance your mathematical foundation.
membership symbol
The membership symbol, represented as \( \in \), is used to show that an element is part of a set. For instance, when we write \(3 \in \{1, 3, 5, 8\}\), it means that the number 3 is a member of the set \({1, 3, 5, 8}\). This concept is straightforward but essential for understanding set theory. Knowing how to use the membership symbol helps you communicate the presence or absence of elements within a set efficiently. Try writing a few example statements such as \(7 \in \{2, 4, 7, 9}\) to get the hang of it.
element identification
Identifying elements within a set is a key skill in set theory. To determine if a particular item is in a set, just check if it is listed among the set's elements. For example, given the set \( \{1, 3, 5, 8}\ \), identifying whether the number 3 is an element involves simply checking the list. Because 3 is indeed listed, it is part of the set. This simple method can be applied to any set, whether it's numbers, letters, or other objects. Practice with different types of sets to become more comfortable with element identification.

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Most popular questions from this chapter

Locate the given number between two successive integers on the number line. For example, if the given number is \(2.6,\) it is located between 2 and 3 on the number line. $$\frac{-15}{2}$$

Compute the given expression. Round off your answer to two decimal places where necessary. $$ \frac{-12.5}{2.5} $$

Evaluate the given expression. Remember to follow the order of operations. $$48 \div 12 \div 4$$

Consider the following statements. If the statement is true, explain why. If the statement is false, explain why and/or give an example illustrating why. (a) Every rational number is an integer. (b) Every integer is a rational number. (c) \(-15\) is greater than \(-10\) (d) The absolute value of \(-15\) is greater than the absolute value of \(-10 .\) (e) A rational number must be positive. (f) An integer must be positive. (g) Every real number is a rational number. (h) Every rational number is a real number.

Compute the given expression. Round off your answer to two decimal places where necessary. $$5.2-1.4(2.8-0.7)$$
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