Question

A relation $R$ is defined on the set $Z$ of integers as follows: R=$(x,y)$ $\in R:x^2+y^2=25$. Express $R$ and $R^{-1}$ as the sets of ordered pairs and hence find their respective domains.

• A. $0$
• B. Domain of $R=\{0,\pm 3\}=$ domain of $R^{-1}.$
• C. Domain of $R=\{0,\pm 3,\pm 4\}=$ domain of $R^{-1}.$
• D. Domain of $R=\{0,\pm 3,\pm 4,\pm 5\}=$ domain of $R^{-1}.$

Answer 1

The correct option is D Domain of $R=\{0,\pm 3,\pm 4,\pm 5\}=$ domain of $R^{-1}.$

$R=\{(0,5),(0,-5),(3,4),(-3,4),(3,-4),(-3,-4),(4,3),(-4,3),(4,-3),(-4,3),(5,0),(-5,0)\}{R}^{-1}=\{(5,0),(-5,0),(4,3),(4,-3),(-4,3),(-4,-3),(3,4),(3,-4),(-3,4),(3,-4),(0,5),(0,-5)\}$
Therefore domain of $R\equiv \{0,3,-3,-4,4,-5,-5\}=$ domain of $R^{-1}$