**Subset A: Odd Numbers**

To create a subset A of N (the set of numbers from 1 to 100) that contains only odd numbers, we need to select the odd elements from N.

1. Identify Odd Numbers:
- Odd numbers are integers that cannot be divided evenly by 2.
- In this case, odd numbers from 1 to 100 are: 1, 3, 5, 7, 9, ..., 99.

2. Select Odd Numbers:
- We will pick all the odd numbers from the given range to form subset A.
- Subset A = {1, 3, 5, 7, 9, ..., 99}.

**Subset B: Squares of Natural Numbers**

To create a subset B of N (the set of numbers from 1 to 100) that contains the squares of natural numbers, we need to represent each element x of N as x^2.

1. Identify Natural Numbers:
- Natural numbers are positive integers starting from 1 and extending infinitely.
- In this case, natural numbers from 1 to 100 are: 1, 2, 3, 4, ..., 100.

2. Calculate Squares:
- For each natural number x in the given range, calculate its square (x^2).
- Square of a number x is obtained by multiplying x by itself.
- Subset B = {1^2, 2^2, 3^2, 4^2, ..., 100^2}.

3. Calculate Squares:
- Simplify the squares:
- 1^2 = 1
- 2^2 = 4
- 3^2 = 9
- 4^2 = 16
- ...
- 100^2 = 10,000

4. Final Subset B:
- Subset B = {1, 4, 9, 16, ..., 10,000}.

By following the above steps, we have successfully created subset A (odd numbers) and subset B (squares of natural numbers) from the set N={1,2,3,...,100}. These subsets satisfy the given conditions and contain the required elements.

A= {1,3,5...}
b= {2^2, 3^2...}