Question

Determine whether or not each of the following is a partition of set N of natural numbers. (With reason)

Answer 1

Only Set B  is a partition of set N of natural numbers .

What are 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.

To know more about Natural Numbers

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