Question

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relation 2 relation 3
{(n, y), (g, g), (y, z), (z, y)}
each relation that represents a functio

Explanation:

To determine if a relation is a function, we use the definition: a relation is a function if each input (first element of the ordered pair) has exactly one output (second element of the ordered pair).

Step 1: Identify the inputs (domains)

The ordered pairs in Relation 3 are \((n, y)\), \((g, g)\), \((y, z)\), \((z, y)\). The inputs (first elements) are \(n\), \(g\), \(y\), \(z\).

Step 2: Check for unique outputs

• For input \(n\), the output is \(y\) (only one output).
• For input \(g\), the output is \(g\) (only one output).
• For input \(y\), the output is \(z\) (only one output).
• For input \(z\), the output is \(y\) (only one output).

Since each input has exactly one output, this relation satisfies the definition of a function.

Answer:

This relation (Relation 3) is a function because every input (first element of each ordered pair) has exactly one output (second element of each ordered pair).