Questions: (u, b),(n, v),(v, b),(b, b) Function Not a function

Solution Steps

To determine if a relation is a function, we need to check if each input (first element of each pair) is associated with exactly one output (second element of each pair). If any input is associated with more than one output, the relation is not a function.

1. Extract the first elements of each pair to identify the inputs.
2. Check if any input is repeated with a different output.

The given relation is a set of ordered pairs: \[ \{(v, b), (b, b), (n, v), (u, b)\} \]

For each ordered pair \((x, y)\), \(x\) is the input and \(y\) is the output. We list the inputs and their corresponding outputs:

• Input \(v\) maps to output \(b\)
• Input \(b\) maps to output \(b\)
• Input \(n\) maps to output \(v\)
• Input \(u\) maps to output \(b\)

A relation is a function if each input is associated with exactly one output. We check if any input is repeated with a different output:

• Input \(v\) maps to one output \(b\)
• Input \(b\) maps to one output \(b\)
• Input \(n\) maps to one output \(v\)
• Input \(u\) maps to one output \(b\)

Since no input is associated with more than one output, the relation satisfies the criteria for being a function.

Final Answer