Math Problem Statement
A={1,2,{3,4},{5,6,7}}
Select the true statement.
Group of answer choices
{1,2}⊆A
{3}∈A
{3,4}⊆A
{1,2}∈A
Solution
Let's go through the given set and evaluate each statement:
-
:
- This statement is asking whether the set is a subset of . For this to be true, every element of must be an element of .
- The set contains the elements , , , and . Since and are elements of , this statement is true.
-
:
- This statement asks whether the set is an element of . Notice that contains , but not . So, this statement is false.
-
:
- This statement asks whether the set is a subset of . For this to be true, both and must be elements of . However, and are contained in the set , which is an element of , but and are not direct elements of . So, this statement is false.
-
:
- This statement asks whether the set is an element of . Since contains the elements , , , and , and is not one of the elements in , this statement is false.
Conclusion:
The true statement is:
Would you like further explanation on these concepts? Here are some related questions you might find interesting:
- What is the difference between a set being a subset and an element of another set?
- How do you distinguish between an element and a subset when working with sets?
- What is the meaning of and in set theory?
- How do you determine if a set is a proper subset of another set?
- What is the difference between and in set notation?
Tip: Always remember that means "is a subset of" (including the possibility of being equal), while means "is an element of".
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Math Problem Analysis
Mathematical Concepts
Set Theory
Subset
Element of a Set
Formulas
-
Theorems
Subset Definition
Element of a Set Definition
Suitable Grade Level
Grades 8-10