State, whether the following pairs of sets are equal or not:
`M={x:x in W " and x+3 lt 8}` and `N={y:y = 2n-1, n in N " and " n lt 5}`

Answer

To determine whether the sets \( M \) and \( N \) are equal, we will analyze each set step by step.

### Step 1: Define Set \( M \)

Set \( M \) is defined as:
\[ M = \{ x : x \in W \text{ and } x + 3 < 8 \} \]
where \( W \) is the set of whole numbers.

**Finding the values of \( x \)**:
1. Start with the inequality:
\[ x + 3 < 8 \]
2. Subtract 3 from both sides:
\[ x < 5 \]
3. Since \( x \) is a whole number, the possible values for \( x \) are:
\[ 0, 1, 2, 3, 4 \]
4. Therefore, we can write:
\[ M = \{ 0, 1, 2, 3, 4 \} \]

### Step 2: Define Set \( N \)

Set \( N \) is defined as:
\[ N = \{ y : y = 2n - 1, n \in N \text{ and } n < 5 \} \]
where \( N \) is the set of natural numbers.

**Finding the values of \( y \)**:
1. The natural numbers less than 5 are:
\[ 1, 2, 3, 4 \]
2. Now, substitute these values into the equation \( y = 2n - 1 \):
- For \( n = 1 \):
\[ y = 2(1) - 1 = 1 \]
- For \( n = 2 \):
\[ y = 2(2) - 1 = 3 \]
- For \( n = 3 \):
\[ y = 2(3) - 1 = 5 \]
- For \( n = 4 \):
\[ y = 2(4) - 1 = 7 \]
3. Therefore, we can write:
\[ N = \{ 1, 3, 5, 7 \} \]

### Step 3: Compare Sets \( M \) and \( N \)

Now we have:
- \( M = \{ 0, 1, 2, 3, 4 \} \)
- \( N = \{ 1, 3, 5, 7 \} \)

**Check for equality**:
1. The elements of set \( M \) are \( 0, 1, 2, 3, 4 \).
2. The elements of set \( N \) are \( 1, 3, 5, 7 \).
3. Since the elements in both sets are not the same, we conclude:
\[ M \neq N \]

### Final Answer
The sets \( M \) and \( N \) are not equal.

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