<p>Let <i>A</i> and <i>B</i> be two sets containing 2 elements and 4 elements respectively. The number of subsets of <i>A</i> × <i>B</i> having 3 or more elements is</p>
Step-by-Step Solution
Key Concept: The total number of subsets of A × B is 2^(|A|×|B|), and we must subtract subsets with 0, 1, or 2 elements to find those with 3 or more elements.
<p><strong>Step 1:</strong> Find |A × B|. Since |A| = 2 and |B| = 4, we have |A × B| = 2 × 4 = 8 elements.</p><p><strong>Step 2:</strong> Total number of subsets of A × B = 2^8 = 256.</p><p><strong>Step 3:</strong> Count subsets with fewer than 3 elements (i.e., 0, 1, or 2 elements):</p><ul><li>Subsets with 0 elements: C(8,0) = 1</li><li>Subsets with 1 element: C(8,1) = 8</li><li>Subsets with 2 elements: C(8,2) = 28</li></ul><p><strong>Step 4:</strong> Total subsets with 0, 1, or 2 elements = 1 + 8 + 28 = 37.</p><p><strong>Step 5:</strong> Subsets with 3 or more elements = 256 - 37 = <strong>219</strong>.</p><p>∴ Answer: D</p>
Correct Answer: D