Final answer:
A mathematical partition of set a = {1,2,...,10} with |p| = 3 could be P1 = {1,2,3,4}, P2 = {5,6,7}, and P3 = {8,9,10}, where each subset contains unique elements from a and all elements are included.
Step-by-step explanation:
In mathematics, a partition of a set is a grouping of its elements into non-empty subsets, in such a way that every element is included in exactly one subset. For the set a = {1,2,...,10}, a partition of a such that the number of parts or blocks in the partition, denoted as |p|, equals 3 can be given by:
- P1 = {1,2,3,4}
- P2 = {5,6,7}
- P3 = {8,9,10}
Each subset P1, P2, and P3 contains elements from the set a and together they include all elements of a without overlap. This is one of many possible partitions of the set a into three parts.