Let N be the set of natural numbers. Describe the following relations in words, giving their domain and the range. `{(2,1),(4,2),(10,5),(18,9),(20,10)}`

Answer

To describe the given relation and identify its domain and range, we can follow these steps:

### Step 1: Understand the Relation
The given relation is a set of ordered pairs:
\[ \{(2,1), (4,2), (10,5), (18,9), (20,10)\} \]
Each ordered pair consists of an element from the first component (x) and an element from the second component (y).

### Step 2: Identify the Domain
The domain of a relation is the set of all first elements (x-values) from the ordered pairs.

From the given relation:
- The first elements (x-values) are: 2, 4, 10, 18, and 20.

Thus, the domain is:
\[ \text{Domain} = \{2, 4, 10, 18, 20\} \]

### Step 3: Identify the Range
The range of a relation is the set of all second elements (y-values) from the ordered pairs.

From the given relation:
- The second elements (y-values) are: 1, 2, 5, 9, and 10.

Thus, the range is:
\[ \text{Range} = \{1, 2, 5, 9, 10\} \]

### Step 4: Describe the Relation in Words
The relation can be described as follows:
- Each element in the domain is related to an element in the range such that the second element is half of the first element. In other words, for any ordered pair \((x, y)\) in the relation, \(y\) is equal to half of \(x\).

### Final Summary
- **Domain**: \{2, 4, 10, 18, 20\}
- **Range**: \{1, 2, 5, 9, 10\}
- **Description**: The relation pairs each natural number \(x\) with \(y\) such that \(y\) is half of \(x\).

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