Home
Class 12
MATHS
Let A=[1,2,3], B=[1,3,5]. If relation R ...

Let A=[1,2,3], B=[1,3,5]. If relation R from A to B is given by R={(1,3),(2,5),(3,3)}. Then `R^(-1)` is: is:

A

{(3,3),(3,1),(5,2)}

B

{(1,3),(2,5),(3,3)}

C

{(1,3),(5,2)}

D

None of the above

Text Solution

AI Generated Solution

The correct Answer is:
To find the inverse of the relation \( R \) from set \( A \) to set \( B \), we follow these steps: 1. **Identify the relation \( R \)**: The relation \( R \) is given as: \[ R = \{(1, 3), (2, 5), (3, 3)\} \] 2. **Understand the concept of inverse relation**: The inverse relation \( R^{-1} \) is formed by swapping the elements in each ordered pair of \( R \). This means that if \( (a, b) \) is in \( R \), then \( (b, a) \) will be in \( R^{-1} \). 3. **Swap the pairs**: - For the pair \( (1, 3) \), we get \( (3, 1) \). - For the pair \( (2, 5) \), we get \( (5, 2) \). - For the pair \( (3, 3) \), it remains \( (3, 3) \) since both elements are the same. 4. **Write the inverse relation**: Thus, the inverse relation \( R^{-1} \) is: \[ R^{-1} = \{(3, 1), (5, 2), (3, 3)\} \] 5. **Final answer**: Therefore, the inverse relation \( R^{-1} \) is: \[ R^{-1} = \{(3, 1), (5, 2), (3, 3)\} \]
Promotional Banner

Similar Questions

Explore conceptually related problems

" Let "A=(1,2,3),B=(1,3,5)" .If relation "R" from "A" to "B" is given by "((1,3),(2,5),(3,3))" then "R^(-1)" is "

The relation R from A to B is given as R = {(5, 3), (2, 7), (8, 5)}. The range of R is

The relation R from A to B is given as R = {(1, 2), (2, 5), ((1)/(2), 7)} . The domain of R is

Let P={1, 2, 3} and a relation on set P is given by the set R={(1,2),(1,3),(2,1),(1,1),(2,2),(3,3),(2,3)}. Then R is:

Let A={1,2,3,4} and R be a relation in given by R=(1,1),(2,2),(3.3).(4,4),(1,2),(2,1),(3,1),(1,3)} Then R is

Let A={1,2,3} and R=A xx A then the relation R on A is :

Let A={1,2,3,4} and R be a relation in A given by R={(1,1),(2,2),(3,3),(4,4),(1,2),(2,1),(3,1),(1,3)} . Then show that R is reflexive and symmetric but not transitive.

Let A={1,2,3,5,6} and B={1,6,7,8} . Let R be a relation from A to B is defined as R=((a,b):a>b,a in A and b in B} .Then the number of elements in R is

Let A={2,3,4,5} and B={1,3,4}. If R is the relation from A to B given by aRb iff a is a divisor of b. Writt R as a set of ordered pairs.