The relation R from A to B is given as R = {(5, 3), (2, 7), (8, 5)}. The range of R is

Options

A. {5, 2, 8}
B. {3, 7, 5}
C. {2, 3, 5, 7, 8}
D. {2, 3, 5, 7}

Answer

To find the range of the relation \( R \) from set \( A \) to set \( B \), we can follow these steps:

### Step 1: Identify the relation \( R \)
The relation \( R \) is given as:
\[ R = \{(5, 3), (2, 7), (8, 5)\} \]

### Step 2: Understand the components of the relation
In the relation \( R \), each ordered pair consists of an element from set \( A \) (the first element of the pair) and an element from set \( B \) (the second element of the pair).

### Step 3: Extract the second elements
To find the range of the relation \( R \), we need to look at the second elements of each ordered pair. These second elements represent the outputs of the relation, which form the range.

From the pairs:
- From \( (5, 3) \), the second element is \( 3 \).
- From \( (2, 7) \), the second element is \( 7 \).
- From \( (8, 5) \), the second element is \( 5 \).

### Step 4: List the unique second elements
Now, we list the unique second elements we found:
\[ \text{Range of } R = \{3, 7, 5\} \]

### Step 5: Write the final answer
Thus, the range of the relation \( R \) is:
\[ \{3, 7, 5\} \]