Functional Dependency Math Example 3

Follow the full solution, then compare it with the other examples linked below.

Example 3

easy
Does {(1,2),(1,3),(2,4)}\{(1,2), (1,3), (2,4)\} represent a function?

Solution

  1. 1
    Input 11 maps to both 22 and 33.
  2. 2
    No — a function requires each input to have exactly one output.

Answer

No, not a function.
In a set of ordered pairs, a relation is a function only if no input value appears with two different outputs. Here, 1→21 \to 2 and 1→31 \to 3 violates this.

About Functional Dependency

A relationship where the value of one quantity (the output or dependent variable) is completely determined by the value of another quantity (the input or independent variable). If yy depends on xx, then knowing xx uniquely determines yy.

Learn more about Functional Dependency →

More Functional Dependency Examples

Example 1 easy

Is [formula] functionally dependent on [formula] in the equation [formula]?

Example 2 medium

Is [formula] functionally dependent on [formula] in [formula]?

Example 4 medium

In a class, is final grade a function of student name?

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