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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1:21 minutes

Problem 62

Textbook Question

Let A = {2, 4, 6, 8, 10, 12}, B = {2, 4, 8, 10}, C = {4, 10, 12}, D = {2, 10}, andU = {2, 4, 6, 8, 10, 12, 14}. Determine whether each statement is true or false. A ⊆ C

Verified step by step guidance

Identify the elements of set A: \{2, 4, 6, 8, 10, 12\}.

Identify the elements of set C: \{4, 10, 12\}.

Understand that A \subseteq C means every element of A must also be an element of C.

Check each element of A to see if it is in C: 2 is not in C, 4 is in C, 6 is not in C, 8 is not in C, 10 is in C, 12 is in C.

Since not all elements of A are in C, A is not a subset of C, so the statement is false.

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Key Concepts

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

Set Theory

Set theory is a branch of mathematical logic that studies sets, which are collections of objects. In this context, understanding the relationships between sets, such as subsets, unions, and intersections, is crucial. A set A is a subset of set C (denoted A ⊆ C) if every element of A is also an element of C.

Subset Definition

A subset is a set whose elements are all contained within another set. For example, if A = {2, 4, 6} and B = {2, 4, 6, 8}, then A is a subset of B. To determine if A ⊆ C, we must check if all elements of A are present in C, which requires a direct comparison of the elements in both sets.

Element Comparison

Element comparison involves checking whether specific elements of one set exist in another set. In this problem, we need to compare the elements of set A with those of set C. If any element of A is not found in C, then the statement A ⊆ C is false, highlighting the importance of thorough examination of each element.