Question

Consider the following subsets of 𝑆 = {1, 2, 3, … ,8,9}: 

(𝑖) [{1,3,5},{2,4,6,8},{5,7,9}]

(𝑖𝑖) [{1,3,5},{2,4,6,8},{7,9}]

Does 𝑖 and 𝑖𝑖 form a partition on sample space 𝑆 [4]

Answer 1

Solution:

A collection of sets P₁, P₂,...,P_n is said to partition the sample space if the sets (i) are mutually disjoint and (ii) have as union the entire sample space.

But here in (i), the sets are not disjoint as {1,3,5} and {5,7,9} have 5 in common.

So, they do not form a partion on S.

But for (ii), {1,3,5},{2,4,6,8},{7,9} are disjoing as well as they form S.

So, they form a partition on S.