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Suppose that the relation \( G \) is defined as follows. \[ G=\{(6, b),(6, a),(4, c)\} \] Give the domain and range of \( G \). Write your answers using set notation.

Ask by Ryan Ortiz. in the United States
Nov 02,2024

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Answer

\[ \text{Domain}(G) = \{4, 6\} \] \[ \text{Range}(G) = \{a, b, c\} \]

Solution

The domain of a relation is the set of all first elements (or inputs) from the ordered pairs, while the range is the set of all second elements (or outputs). For the relation \( G = \{(6, b), (6, a), (4, c)\} \): - The first elements (domain) are: \( 6, 6, 4 \). When we list them without repetition, the domain is \( \{4, 6\} \). - The second elements (range) are: \( b, a, c \). When we list them without repetition, the range is \( \{a, b, c\} \). Thus, the domain and range of \( G \) are: \[ \text{Domain}(G) = \{4, 6\} \] \[ \text{Range}(G) = \{a, b, c\} \]

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The Deep Dive

The domain of the relation \( G \) consists of all the first elements in each ordered pair. From \( G = \{(6, b),(6, a),(4, c)\} \), we have the first elements as 6 and 4. Therefore, the domain is \( \{4, 6\} \). The range of the relation \( G \) consists of all the second elements in each ordered pair. From the pairs, we have the second elements as \( b, a, \) and \( c \). Thus, the range is \( \{a, b, c\} \). In summary, the domain is \( \{4, 6\} \) and the range is \( \{a, b, c\} \).

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