Question

What is the range of the inverse of relation {(1, 7), (2, -4), (5, 6), (2, 8)}?

{1, 2, 5}


{-4, 6, 7, 8}


{1, 5}


{-4, 7, 8}

Answer 1

{1, 2, 5}

Explanation:

`\{(1,\ 7),\ (2,\ -4),\ (5,\ 6),\ (2,\ 8)\}\\\\\text{Domain of given relation:}\ \{1,\ 2,\ 5\}\\\text{Range of given relation:}\ \{-4,\ 6,\ 7,\ 8\}\\\\\text{The inverse}\ R^(-1),\text{ of a relation}\ R\ \text{ is the set of ordered pairs obtained}\\\text{by reversing those of}\ R^(-1)=\{(x,\ y):\ (y,\ x)\in R\} \\\\\text{Example:}\\\text{If}\ (x,\ y)\in R,\ \text{then}\ (y,\ x)\in R^(-1)\to (1,\ 3)\in R\to (3,\ 1)\in R^(-1).\\\\\text{Therefore. The range of the inverse relation is}\ \{1,\ 2,\ 5\}`