 If N is set of natural numbers. Let E be set of even natural numbers and O be set of odd 
natural numbers, then find N E  , N O  , E O  , O E  and OE

We are given the following sets:

- \( N \): the set of natural numbers
- \( E \): the set of even natural numbers
- \( O \): the set of odd natural numbers

We need to find:

1. \( N - E \)
2. \( N - O \)
3. \( E - O \)
4. \( O - E \)
5. \( E \cap O \) (intersection of \( E \) and \( O \))

Let's solve these step by step:

### 1. \( N - E \)
This means the set of natural numbers that are not even. By definition, the natural numbers are either even or odd, so \( N - E \) must be the set of odd natural numbers.
\[
N - E = O
\]

### 2. \( N - O \)
This means the set of natural numbers that are not odd. Similarly, natural numbers are either odd or even, so \( N - O \) must be the set of even natural numbers.
\[
N - O = E
\]

### 3. \( E - O \)
This means the set of even numbers that are not odd. Since no number can be both even and odd, every even number is not odd. Therefore, \( E - O \) is just the set of even numbers.
\[
E - O = E
\]

### 4. \( O - E \)
This means the set of odd numbers that are not even. Similarly, no odd number can be even, so \( O - E \) is just the set of odd numbers.
\[
O - E = O
\]

### 5. \( E \cap O \)
This represents the intersection of the sets of even and odd numbers, which is the set of elements that are both even and odd. Since no number is both even and odd, the intersection is the empty set.
\[
E \cap O = \emptyset
\]

### Final answers:
1. \( N - E = O \)
2. \( N - O = E \)
3. \( E - O = E \)
4. \( O - E = O \)
5. \( E \cap O = \emptyset \)

Would you like a more detailed explanation on any of these steps?

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Here are 5 related questions:

1. What is the complement of \( O \) in the universal set of natural numbers?
2. How would you describe the union of \( E \) and \( O \)?
3. What is the result of \( E \cup \emptyset \)?
4. How would you define the symmetric difference of \( E \) and \( O \)?
5. What is the intersection of \( N \) and the empty set?

**Tip:** The complement of a set consists of all elements not in the set, relative to a universal set.

If N is set of natural numbers. Let E be set of even natural numbers and O be set of odd natural numbers, then find N - E, N - O, E - O, O - E, and E ∩ O.

Explore how to solve a set theory problem involving natural numbers, even numbers, and odd numbers. Learn to compute set differences like N - E and N - O, and understand the mutual exclusivity of even and odd numbers. Suitable for Grades 6-8.

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