Let A, B, and C be three subsets of the universal set U. Given the following Venn diagram, which one of the following sets represents the intersection of A and C?
Understand the Problem
The question asks which set represents the intersection of sets C and A based on the provided Venn diagram, involving logical reasoning with the given numbers in the diagram.
Answer
The intersection \( A \cap C \) is \( \{50\} \).
Answer for screen readers
The intersection of sets ( A ) and ( C ) is ( {50} ).
Steps to Solve
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Identify the Sets and Intersection
In the given Venn diagram, we need to find the intersection of sets ( A ) and ( C ). The intersection is characterized by elements that are common to both sets. -
Find Elements in Set A
Set ( A ) contains numbers:- 10 (only in A)
- 70 (in intersection of A and B)
- 50 (in intersection of A and C)
- 60 (only in A)
- Total numbers are 10, 50, 60, 70.
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Find Elements in Set C
Set ( C ) contains the numbers:- 30 (only in C)
- 50 (in intersection of A and C)
- Total numbers are 30, 50.
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Identify Intersection of A and C
The intersection ( A \cap C ) consists of the common elements from both sets ( A ) and ( C ). The only common number between ( A ) and ( C ) is:- 50
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List the Elements of the Intersection
Thus, the final intersection is:
$$ A \cap C = {50} $$
The intersection of sets ( A ) and ( C ) is ( {50} ).
More Information
The intersection set ( A \cap C ) shows elements that are present in both sets. In this case, it's important for logical reasoning, referencing how sets work in a Venn diagram.
Tips
- Not considering elements unique to sets: Sometimes, people confuse intersections with unions. Remember, intersections only include items common to both sets.
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