Question

Use the relation S { (3,4) , (2,3), (1,2), (2,1)} for questions 1 and 2

1. State the domain and range of S
2. Is S a function? Explain your reasoning.

Answer 1

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Explanation:

1. The domain and range of relation S are as follows:

Domain: The domain refers to the set of all input values in a relation. In this case, the domain of S is {3, 2, 1}, which corresponds to the first element of each ordered pair in the relation.

Range: The range refers to the set of all output values in a relation. In this case, the range of S is {4, 3, 2, 1}, which corresponds to the second element of each ordered pair in the relation.

2. No, relation S is not a function.

To be considered a function, each input value (or element in the domain) should have only one corresponding output value (or element in the range). However, in the given relation S, the input value 2 is associated with both the output values 3 and 1.

Since one input value is associated with multiple output values, S fails the definition of a function.