Math Problem Statement

LaTeX: A:=:\lbrace2,4,6,8,10,12,14,16,18,20\rbrace LaTeX: B:=:\lbrace10,12,14,16,18\rbrace Which of the following is true?

LaTeX: A:=:B

LaTeX: A:\cong B

LaTeX: A:\subseteq B

LaTeX: B:\subseteq:A

Solution

Given the sets:

A={2,4,6,8,10,12,14,16,18,20}A = \{2, 4, 6, 8, 10, 12, 14, 16, 18, 20\} B={10,12,14,16,18}B = \{10, 12, 14, 16, 18\}

Let's evaluate the options:

  1. A=BA = B: This statement is false because AA and BB do not have the same elements. Set AA has 10 elements, while set BB has only 5 elements.

  2. ABA \cong B: This symbol, when used in set theory, typically refers to isomorphism, which is not meaningful for basic set equality or subset relations. Thus, this statement is neither applicable nor true in this context.

  3. ABA \subseteq B: This is false because AA contains elements that are not in BB (e.g., 2, 4, 6, 8, 20).

  4. BAB \subseteq A: This statement is true because every element in BB (10, 12, 14, 16, 18) is also in AA.

Hence, the correct statement is:

BAB \subseteq A

Would you like to go over any specific option in more detail or have any further questions?

Related Questions

  1. What is the definition of a subset and a proper subset?
  2. How can we visually represent the relationship between AA and BB?
  3. What is the difference between equality and subset relations in set theory?
  4. What does ABA \cong B usually denote in mathematical contexts outside of set theory?
  5. What are other set operations that can be applied to AA and BB?

Tip: To verify BAB \subseteq A, check if all elements of BB are in AA. This ensures that BB is indeed a subset of AA.

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Math Problem Analysis

Mathematical Concepts

Set Theory
Subsets
Set Equality

Formulas

-

Theorems

Subset Theorem
Set Equality Theorem

Suitable Grade Level

Grades 8-10