Let N be the set of natural numbers. Describe the following relations in words, giving their domain and the range. `{(3,1),(6,2),(15,5)}`

Answer

To describe the relation given by the set of ordered pairs \(\{(3,1),(6,2),(15,5)\}\), we will follow these steps:

### Step 1: Identify the Ordered Pairs
The relation consists of the following ordered pairs:
- (3, 1)
- (6, 2)
- (15, 5)

### Step 2: Define Domain and Range
- **Domain**: The domain of a relation is the set of all first elements (x-values) from the ordered pairs. In this case, the first elements are 3, 6, and 15.
- **Range**: The range of a relation is the set of all second elements (y-values) from the ordered pairs. In this case, the second elements are 1, 2, and 5.

### Step 3: Write the Domain and Range
- **Domain**: The domain of the relation is \(\{3, 6, 15\}\).
- **Range**: The range of the relation is \(\{1, 2, 5\}\).

### Step 4: Describe the Relation in Words
The relation can be described as follows:
- The first element of each ordered pair represents a natural number, while the second element represents a corresponding value that can be derived from the first element. Specifically, for each natural number \(x\) in the domain, there is a unique natural number \(y\) in the range such that:
- \(3\) corresponds to \(1\)
- \(6\) corresponds to \(2\)
- \(15\) corresponds to \(5\)

### Final Summary
The relation is defined as a mapping from the natural numbers 3, 6, and 15 to the natural numbers 1, 2, and 5.

- **Domain**: \(\{3, 6, 15\}\)
- **Range**: \(\{1, 2, 5\}\)

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