Math Problem Statement

Let A = {2, 3, 5, 6, 7, 8} and B = {1, 5, 8}. Indicate if each statement is true or false.

Solution

Let's evaluate each statement given sets A={2,3,5,6,7,8}A = \{2, 3, 5, 6, 7, 8\} and B={1,5,8}B = \{1, 5, 8\}:

  1. 5A5 \in A: True.

    • The number 5 is an element of set AA.
  2. 1B1 \in B: True.

    • The number 1 is an element of set BB.
  3. 8AB8 \in A \cap B: True.

    • The number 8 is an element of both sets AA and BB, so it belongs to their intersection ABA \cap B.
  4. 3B3 \in B: False.

    • The number 3 is not an element of set BB.
  5. ABA \subset B: False.

    • Set AA is not a subset of set BB because AA contains elements (e.g., 2, 3, 6, 7) that are not in BB.

If you have any questions or need further details, feel free to ask!

Here are five related questions to explore further:

  1. What is the union of sets AA and BB?
  2. What is the difference ABA - B?
  3. If C={2,3}C = \{2, 3\}, is CAC \subseteq A?
  4. How many elements are in the intersection ABA \cap B?
  5. What is the complement of AA relative to the universal set UU if U={1,2,3,4,5,6,7,8,9}U = \{1, 2, 3, 4, 5, 6, 7, 8, 9\}?

Tip: When determining if one set is a subset of another, ensure every element in the first set is also in the second set.

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Math Problem Analysis

Mathematical Concepts

Set theory

Formulas

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Theorems

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Suitable Grade Level

High school