Question 27

Mathematics Sets Easy

Let S = {1, 2, ..., n}. The number of possible pairs of the form (A, B) with A ⊆ B for subsets A, B of S is

(A) 2<sup>n</sup>
(B) 3<sup>n</sup>
(C) n!
(D) <span class="math-tex">\({\rm{\Sigma }}_{k = 0}^n\left( {\begin{array}{*{20}{c}} n\\ k \end{array}} \right)\left( {\begin{array}{*{20}{c}} n\\ {n - k} \end{array}} \right)\)</span>
✓ Correct Answer: Option B Verified Solution

📘 Step-by-Step Solution & Detailed Explanation:

The number of possible pairs of subsets - 3<sup>n</sup>

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