Chapter EP, Problem 7.2.2EP

To determine

To calculate: The inverse of the relation $\left\{\left(-3,9\right),\left(-2,4\right),\left(3,9\right),\left(-1,1\right)\right\}$ .

Answer to Problem 7.2.2EP

The inverse of the relationis $\left\{\left(9,-3\right),\left(4,-2\right),\left(9,3\right),\left(1,-1\right)\right\}$ .

Explanation of Solution

Given information:

The relation $\left\{\left(-3,9\right),\left(-2,4\right),\left(3,9\right),\left(-1,1\right)\right\}$ .

Formula used:

Two relations A and B are said to be inverse relations if and only if whenever the relation A contains the element $\left(a,b\right)$ the other relation B contains the element $\left(b,a\right)$ .

Calculation:

Consider the relation $\left\{\left(-3,9\right),\left(-2,4\right),\left(3,9\right),\left(-1,1\right)\right\}$ .

Recall that two relations A and B are said to be inverse relations if and only if whenever the relation A contains the element $\left(a,b\right)$ the other relation B contains the element $\left(b,a\right)$ .

Exchange the coordinates of ordered pairs.

Therefore, inverse of the relations is $\left\{\left(9,-3\right),\left(4,-2\right),\left(9,3\right),\left(1,-1\right)\right\}$ .