To determine whether the relation {1, 3, 4, 0, 3, 1, 0, 4, 2, 3} is a function, we need to understand what a function is in mathematical terms.
A relation is considered a function if every input (or ‘x’ value) is associated with exactly one output (or ‘y’ value). In other words, for each unique ‘x’ in the set, there should not be multiple corresponding ‘y’ values.
Let’s analyze the given relation: {1, 3, 4, 0, 3, 1, 0, 4, 2, 3}.
1. **Identify Unique Inputs**: We can interpret these numbers as pairs where the first number represents the input and the second number represents the output (e.g., (x, y)). However, the relation provided appears to be a single set of numbers without clear pairing, which is typically how relations are represented.
2. **Examine the Values**: If we break this down into unique values, we have the numbers {0, 1, 2, 3, 4}. Each number only appears once in this case. However, when we look at how some of these might repeat or combine as (x, y) placeholders, it gets tricky.
3. **Checking for Duplicates**: If we assume that the relation pairs unique inputs with unique outputs, we see that the numbers 0, 1, 3, and 4 repeat in terms of how many times they could interact with other potentials in relation. For instance, if we paired them as such:
(1, y1), (3, y2), (4, y3), (0, y4), (2, y5), and so on.
This doesn’t clearly illustrate their relation, as we aren’t defining specific outputs for each input here.
4. **Conclusion**: If these represent isolated sets without pairs indicating unique outputs (like (1, 2), (1, 3)), we can’t directly conclude a function. There are implications of multiple outputs when analyzing pairs. Therefore, based on the uncertainty and assumptions made regarding the duplicates, we can conclude:
No, the relation {1, 3, 4, 0, 3, 1, 0, 4, 2, 3} is not a function. This is because it does not adhere to the definition of a function where each input must map to exactly one output, given the potential for duplicate associations.