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Chapter 2: Problem 127

Give an example of a relation with the following characteristics: The relation is a function containing two ordered pairs. Reversing the components in each ordered pair results in a relation that is not a function.

Short Answer

Expert verified
A relation that satisfies the conditions of the exercise: {(1,2), (3,4)}. After reversing the ordered pairs, it becomes {(2,1), (4,3)}, which is not a function.

Step by step solution

01

Understand what a function is

A function is a relation between a set of inputs and a set of permissible outputs such that each input is related to exactly one output. An example of a function might be: {(1,2), (3,4)}. Here each input (1, 3) is related to exactly one output (2, 4).
02

Create a relation that is not a function with reversed components

Next, reverse the ordered pairs from the function you created in Step 1. In our case, it will be {(2,1), (4,3)}. The reversed relation is not a function because there is more than one output for the same input, which violates the definition of a function.
03

Verify the results

Now it's time to check whether the results meet the exercise's criteria. The original relation {(1,2), (3,4)} is a function, and the reversed relation {(2,1), (4,3)} is not a function.

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