Chapter 4, Problem 20CT

To determine

To find: the difference between relation and function and is every relation a function or is every function is relation.

Answer to Problem 20CT

Every relation is not a function and every function a relation.

Explanation of Solution

Given:

A relation and function.

Concept used:

A relation shows the relationship between input and output.

Whereas, a function is type of relation which derives one output for each given input.

All function is relation, but not all relations are functions.

Calculation:

A relation is a relationship between sets of values. Or, it is a subset of the cartesian profuct.

A function is a relation in which there is only one output for each input.

A relation is denoted by $R$ and a function is denoted by $F$ .

Every

Example:

  $R=\left\{\left(2,x\right),\left(9,y\right),\left(2,z\right)\right\}\text{ and }F=\left\{\left(2,x\right),\left(9,y\right),\left(2,z\right)\right\}$ .

The given example is not a function, as $2$ is input for both $x\text{ and }z$ but it’s a relation.

Hence, relation is not a function and every function a relation.