State, whether the following pairs of sets are equivalent or not:
`A={x:x in N " and " 11 ge 2x -1}` and `B={y:y in W " and " 3 le y le 9}`

Answer

To determine whether the sets \( A \) and \( B \) are equivalent, we need to find the elements of each set and compare them.

### Step 1: Define Set A
Set \( A \) is defined as:
\[ A = \{ x : x \in \mathbb{N} \text{ and } 11 \geq 2x - 1 \} \]

To find the elements of set \( A \), we need to solve the inequality \( 11 \geq 2x - 1 \).

### Step 2: Solve the Inequality for Set A
Starting with the inequality:
\[ 11 \geq 2x - 1 \]

Add \( 1 \) to both sides:
\[ 11 + 1 \geq 2x \]
\[ 12 \geq 2x \]

Now, divide both sides by \( 2 \):
\[ 6 \geq x \]
or
\[ x \leq 6 \]

Since \( x \) must be a natural number (\( \mathbb{N} \)), the possible values of \( x \) are:
\[ 1, 2, 3, 4, 5, 6 \]

Thus, we have:
\[ A = \{ 1, 2, 3, 4, 5, 6 \} \]

### Step 3: Define Set B
Set \( B \) is defined as:
\[ B = \{ y : y \in \mathbb{W} \text{ and } 3 \leq y \leq 9 \} \]

Where \( \mathbb{W} \) represents whole numbers. The values of \( y \) that satisfy this condition are:
\[ 3, 4, 5, 6, 7, 8, 9 \]

Thus, we have:
\[ B = \{ 3, 4, 5, 6, 7, 8, 9 \} \]

### Step 4: Compare Sets A and B
Now we compare the elements of sets \( A \) and \( B \):
- Set \( A = \{ 1, 2, 3, 4, 5, 6 \} \)
- Set \( B = \{ 3, 4, 5, 6, 7, 8, 9 \} \)

### Step 5: Determine if the Sets are Equivalent
Two sets are equivalent if they have the same number of elements.

- Set \( A \) has \( 6 \) elements: \( 1, 2, 3, 4, 5, 6 \)
- Set \( B \) has \( 7 \) elements: \( 3, 4, 5, 6, 7, 8, 9 \)

Since the number of elements in set \( A \) is not equal to the number of elements in set \( B \), we conclude that the sets are not equivalent.

### Final Answer
The sets \( A \) and \( B \) are **not equivalent**.

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