Only Set B is a partition of set N of natural numbers .
Numbers starting from 1 to infinity comes under Natural Numbers.
It is asked in the question that to determine whether or not each of the following is a partition of set N of natural numbers
A ) {{n | n > 5}, {n | n < 5}]
It is not a set of natural numbers as it does not include 5.
B ) [{n | n ≥ 6}, {1, 3,5} , {2, 4}]
{1,3,5} {2,4}and {n|n≥6} include all the natural numbers
Therefore , it forms a partition of N.
C ) {{n | n^2 > 11}, {n | n^2 < 11}
Every natural number n must satisfy either n^2 > 11 or n^2 < 11
This cannot be possible , therefore it is not the partition of Natural Numbers.
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