Question

To determine collections of subsets are partitions of \(\{ 1,2,3,4,5,6\} \).

Short answer

The collection of subsets \(\{ \{ 1,4,5\} ,\{ 2,6\} \} \) is not a partition of set.

Step-by-step solution

Given data

The set is \(\{ 1,2,3,4,5,6\} \).

Concept used of partition of sets

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

Find partition of set

The set is \(\{ 1,2,3,4,5,6\} \).

Let \(S = \{ 1,2,3,4,5,6\} \)

Check \(\{ \{ 1,4,5\} ,\{ 2,6\} \} \) is a partition of \(\{ 1,2,3,4,5,6\} \).

This is not a partition of set \(S\) because \(\{ 1,4,5\} \cup \{ 2,6\} \ne S\).

Hence, the collection of subsets \(\{ \{ 1,4,5\} ,\{ 2,6\} \} \) is not a partition of set.