Math Problem Statement

Write a set equivalant to AUC 2. write a set equivalent to AnC

Write a set equivalent to AUC. Write a set equivalent to AnC.

Solution

1. Set Equivalent to ACA \cup C:

  • AA is defined as the set of natural numbers less than 20 that are divisible by 3:
    A={3,6,9,12,15,18}A = \{3, 6, 9, 12, 15, 18\}

  • CC is defined as the set of natural numbers less than 20 that are multiples of 6:
    C={6,12,18}C = \{6, 12, 18\}

  • The union of AA and CC, denoted as ACA \cup C, includes all elements in either AA or CC:
    AC={3,6,9,12,15,18}A \cup C = \{3, 6, 9, 12, 15, 18\}

2. Set Equivalent to ACA \cap C:

  • The intersection of AA and CC, denoted as ACA \cap C, includes only the elements common to both AA and CC:
    AC={6,12,18}A \cap C = \{6, 12, 18\}

Let me know if you'd like more details or have any other questions!

Additional Questions:

  1. What would be the union of BB and CC (BCB \cup C)?
  2. What would be the intersection of AA and BB (ABA \cap B)?
  3. What would be the union of all three sets ABCA \cup B \cup C?
  4. What would be the intersection of all three sets ABCA \cap B \cap C?
  5. Can you list the elements of ABA \setminus B (elements in AA but not in BB)?

Tip:

When working with unions and intersections of sets, using Venn diagrams is a great way to visualize and identify common elements quickly.

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Math Problem Analysis

Mathematical Concepts

Set Theory
Union of Sets
Intersection of Sets

Formulas

A ∪ C (Union of A and C)
A ∩ C (Intersection of A and C)

Theorems

Union and Intersection of Sets

Suitable Grade Level

Grades 6-8