Let `S={1,,2,34}` . The total number of unordered pairs of disjoint subsets of `S` is equal a.`25` b. `34` c. `42` d. `41`

Options

A. 25
B. 34
C. 42
D. 41

Answer

D

Explanation

For disoint sets, `AnnB=phi`
Each element in either A or B or neither.
`therefore` Total ways `=3^(4)=81,A=B" iff "A=B=phi`
Otherwise, A and B are interchangable
`therefore` Number of unordered pair for disoint subsets of
`S=(3^(4)+1)/(2)=41`