Question

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
1. 2ⁿ
2. 3ⁿ
3. n!
4. \({\rm{\Sigma }}_{k = 0}^n\left( {\begin{array}{*{20}{c}} n\\ k \end{array}} \right)\left( {\begin{array}{*{20}{c}} n\\ {n - k} \end{array}} \right)\)

Answer 1

Correct Answer - Option 1 : 2ⁿ

Concept:

Let A be a finite set having n elements. Then, the number of subsets of A is given by: 2n.