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Let S={1,,2,34} . The total number of un...

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`

A

25

B

34

C

42

D

41

Text Solution

Verified by Experts

The total number of ordered pairs of disjoint sub-sets of S, except ordered pair `(phi,phi)` is
`(""^(4)C_(0)xx2^(4)+""^(4)C_(1)xx2^(3)+""^(4)C_(2)xx2^(2)+""^(4)C_(3)xx2^(1)+""^(4)C_(4)xx2^(0))-1`
`=(1+2)^(4)-1=80`
`:.` Required of unodered pairs of disjoint subsets of S is to `(80)/(2)+1=41`.
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