Sets, Relations & Functions
Cartesian Product
Grade 11
Question:
<p>If <span class="latex">A = \{2, 3, 5\}</span>, <span class="latex">B = \{2, 5, 6\}</span>, then <span class="latex">(A \setminus B) \times (A \cap B)</span> is</p>
<p>(a) <span class="latex">\{(3, 2), (3, 3), (3, 5)\}</span></p>
<p>(b) <span class="latex">\{(3, 2), (3, 5), (3, 6)\}</span></p>
<p>(c) <span class="latex">\{(3, 2), (3, 5)\}</span></p>
<p>(d) None of these</p>
Step-by-Step Solution
Key Concept: The set difference A ∖ B contains only elements unique to A. The Cartesian product pairs each element of the first set with all elements of the second set.
<p><strong>Step 1:</strong> Find <span class="latex">A \setminus B = \{3\}</span> (elements in A but not in B)</p><p><strong>Step 2:</strong> Find <span class="latex">A \cap B = \{2, 5\}</span> (common elements)</p><p><strong>Step 3:</strong> Compute Cartesian product <span class="latex">(A \setminus B) \times (A \cap B) = \{3\} \times \{2, 5\} = \{(3, 2), (3, 5)\}</span></p><p>∴ Answer is (c).</p>
Correct Answer: c