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

Required number
(singleton set) `xx` (singletonest)
`=(""^(4)C_(1)xx""^(3)C_(1))/(2)`
(sigleton set) `xx` (set with 2 elements)
`+(""^(4)C_(2)xx""^(2)C_(2))/(2)`
(empty set)`xx` (one out of 15 subsets)
`+""^(4)C_(0)xx""^(15)C_(1)`
(empty set)`xx` (empty set)
`=6+12overset(+)(+)4+3+overset(1)(15)+1=41`