Questions: Draw a Venn diagram to show the set. (A ∩ B′) ∪ U

Draw a Venn diagram to show the set.
(A ∩ B′) ∪ U
Transcript text: Draw a Venn diagram to show the set. \[ \left(A \cap B^{\prime}\right) \cup U \]
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Solution

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Solution Steps

Step 1: Understand the Set Operation

The given set operation is AB A \cap B' . This represents the intersection of set A A and the complement of set B B .

Step 2: Identify the Complement of Set B

The complement of set B B (denoted as B B' ) includes all elements that are not in B B .

Step 3: Determine the Intersection

The intersection AB A \cap B' includes all elements that are in set A A but not in set B B .

Step 4: Analyze the Venn Diagram Options
  • The first diagram shades the part of A A that does not intersect with B B .
  • The second diagram shades the intersection of A A and B B .
  • The third diagram shades the part of B B that does not intersect with A A .
  • The fourth diagram shades the part of B B that does not intersect with A A .

Final Answer

The correct Venn diagram is the first one, which shades the part of A A that does not intersect with B B .

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