State, whether the following pairs of sets are equal or not:
`A={2,4,6,8}` and `B={2n : n in N " and " n le 4}`

Answer

To determine whether the sets \( A \) and \( B \) are equal, we need to follow these steps:

### Step 1: Identify the sets
We have:
- Set \( A = \{2, 4, 6, 8\} \)
- Set \( B = \{2n : n \in \mathbb{N} \text{ and } n \leq 4\} \)

### Step 2: Calculate the elements of set \( B \)
To find the elements of set \( B \), we need to substitute the values of \( n \) from the natural numbers that are less than or equal to 4. The natural numbers \( n \) that satisfy this condition are \( 1, 2, 3, \) and \( 4 \).

Now, we calculate \( 2n \) for each of these values:
- For \( n = 1 \): \( 2 \times 1 = 2 \)
- For \( n = 2 \): \( 2 \times 2 = 4 \)
- For \( n = 3 \): \( 2 \times 3 = 6 \)
- For \( n = 4 \): \( 2 \times 4 = 8 \)

Thus, the elements of set \( B \) are:
\[ B = \{2, 4, 6, 8\} \]

### Step 3: Compare the sets
Now we compare the two sets:
- Set \( A = \{2, 4, 6, 8\} \)
- Set \( B = \{2, 4, 6, 8\} \)

Both sets contain the same elements.

### Step 4: Conclusion
Since both sets \( A \) and \( B \) have the same elements, we conclude that:
\[ A = B \]

### Final Answer
Yes, the sets \( A \) and \( B \) are equal.

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