Given that E= {2,4,6,8,10} .If n represents any members of E , then write the following sets containing all numbers represented by:
(i) n+1
(ii) `n^(2)`.

Answer

To solve the problem, we need to create two sets based on the elements of the given set \( E = \{2, 4, 6, 8, 10\} \). We will define the sets based on the expressions \( n + 1 \) and \( n^2 \), where \( n \) represents any member of the set \( E \).

### Step 1: Define the set \( E \)
The set \( E \) is given as:
\[ E = \{2, 4, 6, 8, 10\} \]

### Step 2: Create the set for \( n + 1 \)
We need to create a new set where each element is obtained by adding 1 to each element of set \( E \).

- For \( n = 2 \): \( n + 1 = 2 + 1 = 3 \)
- For \( n = 4 \): \( n + 1 = 4 + 1 = 5 \)
- For \( n = 6 \): \( n + 1 = 6 + 1 = 7 \)
- For \( n = 8 \): \( n + 1 = 8 + 1 = 9 \)
- For \( n = 10 \): \( n + 1 = 10 + 1 = 11 \)

Now, we can write the set containing all these results:
\[ A = \{3, 5, 7, 9, 11\} \]

### Step 3: Create the set for \( n^2 \)
Next, we create another set where each element is obtained by squaring each element of set \( E \).

- For \( n = 2 \): \( n^2 = 2^2 = 4 \)
- For \( n = 4 \): \( n^2 = 4^2 = 16 \)
- For \( n = 6 \): \( n^2 = 6^2 = 36 \)
- For \( n = 8 \): \( n^2 = 8^2 = 64 \)
- For \( n = 10 \): \( n^2 = 10^2 = 100 \)

Now, we can write the set containing all these results:
\[ B = \{4, 16, 36, 64, 100\} \]

### Final Result
Thus, the two sets we have created are:
- \( A = \{3, 5, 7, 9, 11\} \) for \( n + 1 \)
- \( B = \{4, 16, 36, 64, 100\} \) for \( n^2 \)

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