Table of contents

0. Review of Algebra4h 18m
1. Equations & Inequalities3h 18m
2. Graphs of Equations43m
3. Functions2h 17m
4. Polynomial Functions1h 44m
5. Rational Functions1h 23m
6. Exponential & Logarithmic Functions2h 28m
7. Systems of Equations & Matrices4h 6m
8. Conic Sections2h 23m
9. Sequences, Series, & Induction1h 22m
10. Combinatorics & Probability1h 45m

0. Review of Algebra

Exponents

College Algebra

0. Review of Algebra

Exponents

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0:40 minutes

Problem 38

Textbook Question

Insert ∈ or ∉ in each blank to make the resulting statement true. ∅ ____ ∅

Verified step by step guidance

Understand the symbols: ∅ represents the empty set, which is a set with no elements.

The symbol ∈ means 'is an element of', and ∉ means 'is not an element of'.

Consider the statement: ∅ ∈ ∅. This would mean the empty set is an element of itself, which is not true because the empty set has no elements.

Consider the statement: ∅ ∉ ∅. This means the empty set is not an element of itself, which is true because the empty set contains no elements.

Therefore, the correct symbol to insert is ∉, making the statement ∅ ∉ ∅ true.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Set Membership

Set membership refers to the relationship between an element and a set, denoted by the symbol '∈' (element of) or '∉' (not an element of). If an element is part of a set, we use '∈', while '∉' indicates that the element is not included in the set. Understanding this concept is crucial for determining the validity of statements regarding elements and sets.

Empty Set

The empty set, denoted as '∅', is a unique set that contains no elements. It is a fundamental concept in set theory, representing the idea of 'nothingness' in terms of sets. Recognizing that the empty set has no members is essential for correctly interpreting statements about set membership.

Logical Statements in Set Theory

Logical statements in set theory involve assertions about the relationships between sets and their elements. In this context, determining whether '∅' is an element of itself requires understanding the nature of sets and their elements. Since the empty set contains no elements, it cannot contain itself, making the statement '∅ ∉ ∅' true.