Let S = {1, 2, 3, 4). The total number of unordered pairs of disjoint subsets of S is equal to

Engineering

Mathematics

Permutation and Combination Basic Definitions

Question

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{1, 2, 3, 4}

{1} $\to_{}^{}$ 4

{1, 2} $\to_{}^{}$ ⁴C₂ = 6

{1, 2, 3} $\to_{}^{}$ ⁴C1 = 4

{1, 2, 3, 4} $\to_{}^{}$ 1

A $\to_{}^{}$ One element – 4

B $\to_{}^{}$ Two element – ⁴C₂ = 6

C $\to_{}^{}$ Three element – ⁴C₄ = 4

D $\to_{}^{}$ Four element – ⁴C₄ = 1

E $\to_{}^{}$ No elements $\to_{}^{}$ f

Pairs from (A) = ⁴C₂ = 6

Pairs from (B) = $\frac{^{4} C_{2}}{3} = 3$

Pairs from (C) = 0

Pairs from (D) = 0

Pairs from E + (A, B, C, D) = 0

Pairs from (A – B) = 3

4 × 3 = 12

1 × 4 = 4

Total = 25