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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1:28 minutes

Problem 66

Textbook Question

Insert ⊆ or s in each blank to make the resulting statement true. {5, 6, 7, 8} ____ {1, 2, 3, 4, 5, 6, 7}

Verified step by step guidance

Identify the elements in each set. The first set is {5, 6, 7, 8} and the second set is {1, 2, 3, 4, 5, 6, 7}.

Compare the elements of the first set to the elements of the second set to determine if all elements of the first set are also in the second set.

Notice that the elements 8 from the first set is not present in the second set.

Recall the definition of subset: A set A is a subset of set B if all elements of A are also elements of B.

Since not all elements of the first set are in the second set, the correct symbol to use between these sets is \( \not\subseteq \) (not a subset).

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Key Concepts

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

Set Notation

Set notation is a mathematical language used to describe collections of objects, known as elements. In this context, sets are represented by curly braces, and elements are listed within them. Understanding how to read and interpret set notation is crucial for determining relationships between sets, such as subset and superset.

Subset and Superset

A subset is a set where all its elements are also contained within another set. Conversely, a superset contains all elements of a subset. The symbols '⊆' and 's' are used to denote these relationships, with '⊆' indicating that one set is a subset of another, and 's' indicating that one set is a superset of another.

Element Inclusion

Element inclusion refers to whether an element from one set is also present in another set. This concept is fundamental when determining subset and superset relationships. For example, if every element of set A is found in set B, then A is a subset of B, which is essential for correctly filling in the blanks in the given statement.