Math  /  Discrete

QuestionSuppose that the relation TT is defined as follows. T={(4,5),(8,8),(4,1)}T=\{(4,5),(8,8),(4,-1)\}
Give the domain and range of TT. Write your answers using set notation. domain == \square range == \square

Studdy Solution

STEP 1

1. The relation TT is a set of ordered pairs (x,y)(x, y).
2. The domain of TT is the set of all first elements of these ordered pairs.
3. The range of TT is the set of all second elements of these ordered pairs.

STEP 2

1. Identify the domain of TT by extracting all the first elements of the ordered pairs.
2. Identify the range of TT by extracting all the second elements of the ordered pairs.

STEP 3

Extract the first elements from each ordered pair in TT to form the domain.
T={(4,5),(8,8),(4,1)} T = \{(4,5), (8,8), (4,-1)\}
The first elements are 44, 88, and 44.

STEP 4

Since sets do not contain duplicate elements, the domain of TT is:
domain={4,8} \text{domain} = \{4, 8\}

STEP 5

Extract the second elements from each ordered pair in TT to form the range.
T={(4,5),(8,8),(4,1)} T = \{(4,5), (8,8), (4,-1)\}
The second elements are 55, 88, and 1-1.

STEP 6

Since sets do not contain duplicate elements, the range of TT is:
range={5,8,1} \text{range} = \{5, 8, -1\}
Solution:
domain={4,8} \text{domain} = \{4, 8\} range={5,8,1} \text{range} = \{5, 8, -1\}

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