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Let  S=\{2,3,5,6,8\}  . The total number of unordered pairs of disjoint subsets of S is equal to

Option: 1

121


Option: 2

130


Option: 3

128

 


Option: 4

122


Answers (1)

best_answer

Given that,

S=\{2,3,5,6,8\}

If sets A and B are disjoint sets, then A \cap B=\phi \text {. }

Each component of S may also be a component of either A or B or neither of the subsets.

Each element has three possible configurations.

There are  3^{5}  choices because there are 5 elements.

The total number of ordered pairs of subsets is given by,

3^{5}+1=243+1

3^{5}+1=244

Thus, the total number of unordered pairs is given by,

\frac{244}{2}=122

Therefore, the number of unordered pairs is 122.

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Nehul

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