Let L={ 1,2,3,4,5} be the lattice shown below. Find allsub lattices with three or more elements.
Answers
Answer:
L1,L2,all like this.........,.....
Given : Set L={ 1,2,3,4,5}
To Find : sub sets with three or more elements.
Solution:
L = { 1 , 2 , 3 , 4 , 5}
n(L) = 5
Subsets with elements 3 or more
Means Subsets with elements 3 , 4 or 5
Subsets with 3 elements
3 elements to be selected out of 5 elements
⁵C₃ = 10
Subsets with 4 elements
4 elements to be selected out of 5 elements
⁵C₄ = 5
Subsets with 5 elements
5 elements to be selected out of 5 elements
⁵C₅ = 1
Total Subsets with elements 3 or more
= 10 + 5 + 1
= 16
16 Subsets with three or more elements can be formed from L = { 1 , 2 , 3 , 4 , 5}
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