Let S ={1,2,3,4} The total number of unordered pairs of disjoint subsets of S is equal to 1 25 - Maths - Sets

Question

Let S ={1,2,3,4} The total number of unordered pairs of disjoint
subsets of S is equal to
1 25
2 34
3 42
4 41

Anuradha Sharma · Accepted Answer

Total number of subset of a set of size m is
:2m=∑n=0mm!n!m-n!where the number of subsets of size n of a
set of size m is =m!n!m-n!selecting n elements from m leaves m-n
elements from which disjoint sets of size r can be, formed Thus
thge number of ordered pairs of disjoint subset is,
=∑n=0mm!n!m-n!2m-n=3mHowever, this is for ordered pairs, and
include ϕ,ϕ which is symmetric  We required
unorderedpairs -including ϕ,ϕ so we need to discount
permutaions, =34-12!+1=41

Let S ={1,2,3,4}.The total number of unordered pairs of disjoint subsets of S is equal to 1. 25 2. 34 3. 42 4.41

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

1. 25

2. 34

3. 42

4.41