Chapter 6.2, Problem 13PPS

To determine

The inverse of the relation $\left\{\left(1,-5\right),\left(2,6\right),\left(3,-7\right),\left(4,8\right),\left(5,-9\right)\right\}$ .

Answer to Problem 13PPS

The inverse of the relation $\left\{\left(1,-5\right),\left(2,6\right),\left(3,-7\right),\left(4,8\right),\left(5,-9\right)\right\}$ is $\left\{\left(-5,1\right),\left(6,2\right),\left(-7,3\right),\left(8,4\right),\left(-9,5\right)\right\}$ .

Explanation of Solution

Given information: The given relation $\left(R\right)$ is,

  $R=\left\{\left(1,-5\right),\left(2,6\right),\left(3,-7\right),\left(4,8\right),\left(5,-9\right)\right\}$

Concept used:

The two relations are inverse to each other if and only if one relation has element $\left(p,q\right)$ and the other relation has the element $\left(q,p\right)$ .Mathematically,

  $\text{If }R=\left(p,q\right)\text{ then }{R}^{-1}=\left(q,p\right)$

Calculation: The given relation say $R=\left\{\left(1,-5\right),\left(2,6\right),\left(3,-7\right),\left(4,8\right),\left(5,-9\right)\right\}$ , then inverse relation $\left(R^{-1}\right)$ is written as,

  $R^{-1}=\left\{\left(-5,1\right),\left(6,2\right),\left(-7,3\right),\left(8,4\right),\left(-9,5\right)\right\}$