Question

Let A={1, 2, 3}, B={a, b} and R={(1,b),(3,a),(2,b)} be a relation from A to B. The inverse relation R is _______________________.

• A. $R^{-1}=\left\{\right(a,1),(b,1),(a,3),(b,2\left)\right\}$
• B. $R^{-1}=\left\{\right(2,b),(3,a),(1,b),(1,a\left)\right\}$
• C. $R^{-1}=\left\{\right(b,2),(a,3),(b,1),(a,1\left)\right\}$
• D. All of the above

Answer 1

The correct option is A $R^{-1}=\left\{\right(a,1),(b,1),(a,3),(b,2\left)\right\}$

Let A={1, 2, 3}, B={a, b} and R={(1,b),(3,a),(2,b)} be a relation from A to B. The inverse relation R is-R^-1= {(a,1),(b,1),(a,3),(b,2)}.

Inverse relationshipexists between two variables when one increases the other decreases.

The graph of an inverse relation is the reflection of the original graph over the identity line, y = x. It may be necessary to restrict the domain on certain functions to guarantee that the inverse relation is also a function.