Question

suppose that the relation t is defined as follows. t = {(3, c), (3, d), (6, b)} give the domain and range of t. write your answers using set notation. domain: range:

Explanation:

Step1: Find the domain

The domain of a relation is the set of all first elements (x - values) in the ordered pairs. For the relation \( T=\{(3, c), (3, d), (6, b)\} \), the first elements are 3, 3, and 6. Removing duplicates, the domain elements are 3 and 6. So the domain is \( \{3, 6\} \).

Step2: Find the range

The range of a relation is the set of all second elements (y - values) in the ordered pairs. For the relation \( T=\{(3, c), (3, d), (6, b)\} \), the second elements are \( c \), \( d \), and \( b \). So the range is \( \{b, c, d\} \) (order does not matter in a set).

Answer:

domain: \(\{3, 6\}\)
range: \(\{b, c, d\}\)