Question

To determine collections of subsets are partitions of bit strength of length \(8\).

Short answer

The portions of the set is the union of the set of strings that end with \(00,01,10,11\).

Step-by-step solution

Given data

The set of strings that end with \(111\) , the set of strings that end with \(011\) , the set of strings end with the \(00\) .

Concept used of partition of sets

The set\(S\)in a partition must be nonempty, pair wise disjoint, and have as their union.

Find partition of set

Let us assume

\(X1 = \)The set of strings contains \(3k\) ones

\(X2 = \)The set of strings contains \(3k + 1\) ones

\(X3 = \)The set of strings contains \(3k + 2\) ones

If we observe the intersection of any two sets of sets \(X1,X2,X3\) is empty set.

Therefore, the collection of subsets are partitions of bit strings of length 8 is union of \(X1,X2,X3\).