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

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

Solution

Step 1: Understand the Set Operation

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

Step 2: Identify the Complement of Set B

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

Step 3: Determine the Intersection

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

Step 4: Analyze the Venn Diagram Options

The first diagram shades the part of \( A \) that does not intersect with \( B \).
The second diagram shades the intersection of \( A \) and \( B \).
The third diagram shades the part of \( B \) that does not intersect with \( A \).
The fourth diagram shades the part of \( B \) that does not intersect with \( A \).

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

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