Math Problem Statement

Let A = {1, 2, 3, 4, 5, 8} and B = {1, 2, 8}. Indicate if each statement is true or false.

7∈A

and

B⊂A

Solution

Let's analyze the statements one by one:

  1. 7∈A: This statement means "7 is an element of set A." Looking at set A={1,2,3,4,5,8}A = \{1, 2, 3, 4, 5, 8\}, we see that 7 is not an element of set AA.
    Result: False

  2. B⊂A: This statement means "B is a subset of A." A set BB is a subset of AA if every element of BB is also in AA. Looking at set B={1,2,8}B = \{1, 2, 8\} and set A={1,2,3,4,5,8}A = \{1, 2, 3, 4, 5, 8\}, we see that all elements of BB (1, 2, 8) are in AA.
    Result: True

Would you like further details or have any questions?

Here are 5 related questions to deepen understanding:

  1. What is the difference between a subset and a proper subset?
  2. Can a set be a subset of itself? Why?
  3. What is the complement of set B with respect to set A?
  4. How can we determine the union of sets A and B?
  5. What does the intersection of A and B look like?

Tip: When verifying if one set is a subset of another, check if every element of the smaller set appears in the larger set.

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Math Problem Analysis

Mathematical Concepts

Set Theory
Elements of a Set
Subsets

Formulas

-

Theorems

Subset Definition

Suitable Grade Level

Grades 6-8