Question

To determine collections of subsets are partitions of \(\{ - 3, - 2, - 1,0,1,2,3\} \).

Short answer

The collection of subsets \(\{ \{ - 3,2,3\} ,\{ - 1,1\} \} \) is not a partition of set.

Step-by-step solution

Given data

The set is \(\{ - 3, - 2, - 1,0,1,2,3\} \).

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

The set is \(\{ - 3, - 2, - 1,0,1,2,3\} \).

Let \(S = \{ - 3, - 2, - 1,0,1,2,3\} \)

Check \(\{ \{ - 3,2,3\} ,\{ - 1,1\} \} \) is a partition of \(\{ - 3, - 2, - 1,0,1,2,3\} \).

This is not a partition of set \(S\) because \(\{ - 3,2,3\} \cup \{ - 1,1\} \ne S\).

Hence, the collection of subsets \(\{ \{ - 3,2,3\} ,\{ - 1,1\} \} \) is not a partition of set.