Which of the following Venn diagram represent `(A-B)?`

Options

A.
B.
C.
D.

Answer

To solve the problem of determining which Venn diagram represents \( A - B \), we will follow these steps:

### Step 1: Define the Sets
Let’s define the sets \( A \) and \( B \):
- Set \( A = \{1, 2, 3, 4\} \)
- Set \( B = \{2, 3, 5, 7\} \)

### Step 2: Understand the Operation \( A - B \)
The operation \( A - B \) (also written as \( A \setminus B \)) represents the elements that are in set \( A \) but not in set \( B \). This means we need to remove any elements from set \( A \) that are also present in set \( B \).

### Step 3: Identify Common Elements
Next, we identify the common elements between sets \( A \) and \( B \):
- The common elements are \( 2 \) and \( 3 \).

### Step 4: Subtract the Common Elements
Now, we will subtract the common elements from set \( A \):
- Starting with \( A = \{1, 2, 3, 4\} \)
- Remove \( 2 \) and \( 3 \) (the common elements):

Thus, \( A - B = \{1, 4\} \).

### Step 5: Interpret the Result
The result \( A - B = \{1, 4\} \) indicates that the elements \( 1 \) and \( 4 \) are in set \( A \) but not in set \( B \).

### Step 6: Choose the Correct Venn Diagram
In a Venn diagram:
- The area representing set \( A \) should include \( 1 \) and \( 4 \).
- The area representing set \( B \) should include \( 2 \) and \( 3 \).
- The area that represents \( A - B \) should only include the elements \( 1 \) and \( 4 \) (the part of set \( A \) that does not overlap with set \( B \)).

Thus, the correct Venn diagram will show only the area of set \( A \) that is not overlapping with set \( B \ shaded. ### Conclusion The correct representation of \( A - B \) in the Venn diagram is option B, where only the part of set \( A \) that contains \( 1 \) and \( 4 \) is shaded.

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