Given the universal set `, sum ={x:x in N, 15 lt x le 26}`, list the elements of the following sets:
(i) `A ={x:x gt 20}`, (ii) `B={x : x le 21}`

Answer

To solve the problem, we need to follow these steps:

### Step 1: Identify the Universal Set
The universal set is defined as:
\[ \text{sum} = \{ x : x \in \mathbb{N}, 15 < x \leq 26 \} \]
This means we need to list all natural numbers greater than 15 and less than or equal to 26.

**Elements of the Universal Set:**
- The smallest natural number greater than 15 is 16.
- The largest natural number less than or equal to 26 is 26.
- Therefore, the universal set is:
\[ \text{sum} = \{ 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26 \} \]

### Step 2: Find Set A
Set A is defined as:
\[ A = \{ x : x > 20 \} \]
We need to find elements from the universal set that are greater than 20.

**Elements of Set A:**
- From the universal set, the numbers greater than 20 are:
\[ A = \{ 21, 22, 23, 24, 25, 26 \} \]

### Step 3: Find Set B
Set B is defined as:
\[ B = \{ x : x \leq 21 \} \]
We need to find elements from the universal set that are less than or equal to 21.

**Elements of Set B:**
- From the universal set, the numbers less than or equal to 21 are:
\[ B = \{ 16, 17, 18, 19, 20, 21 \} \]

### Final Results
- The elements of Set A are:
\[ A = \{ 21, 22, 23, 24, 25, 26 \} \]
- The elements of Set B are:
\[ B = \{ 16, 17, 18, 19, 20, 21 \} \]

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