Question

If A = {1, 2, 3, 4, 5) and B = {4, 5, 6, 7}, then A- B=

• A. {2,3}
• B. {4,5}
• C. {1,2,3}
• D. {6,7}

Answer 1

The Correct Option is C

We are tasked with finding the set difference \( A - B \), where:

\[ A = \{1, 2, 3, 4, 5\} \quad \text{and} \quad B = \{4, 5, 6, 7\}. \]

Step 1: Recall the definition of set difference.

The set difference \( A - B \) is the set of elements that belong to \( A \) but do not belong to \( B \). Mathematically:

\[ A - B = \{x \mid x \in A \text{ and } x \notin B\}. \]

Step 2: Identify the elements in \( A \) that are not in \( B \).

The elements of \( A \) are \( \{1, 2, 3, 4, 5\} \), and the elements of \( B \) are \( \{4, 5, 6, 7\} \). The elements \( 4 \) and \( 5 \) are common to both sets, so they are excluded from \( A - B \).

The remaining elements in \( A \) are \( \{1, 2, 3\} \).

Step 3: Write the result.

\[ A - B = \{1, 2, 3\}. \]

Final Answer: The set difference \( A - B \) is \( \mathbf{\{1, 2, 3\}} \), which corresponds to option \( \mathbf{(3)} \).