Let A = {3, 7}, B = {5, 11} and relation R = {(a, b): a ∈ A, b ∈

1.	Let A = {3, 7}, B = {5, 11} and relation R = {(a, b): a ∈ A, b ∈ B and a + b is even} then inverse relation R-1 is 1. Identity relation2. Universal relation3. Empty relation4. Both 1 and 2
Answer» Correct Answer - Option 2 : Universal relation Concept: If R is a relation from set A to set B, then inverse relation of R to be denoted by R-1, is a relation from set B to set A. Symbolically R-1 = {(b, a): (a, b) ∈ R for all a ∈ A and b ∈ B}. A relation R on a set A is said to be identity relation on A if R = {(a, b): a ∈ A, b ∈ A and a = b}. A relation R from A to B is said to be the universal relation, if R = A ×. B A relation R from A to B is called an empty relation or a void relation from A to B if R = ø. Calculation: Given A = {3, 7}, B = {5, 11} Cartesian product \(A× B\) = {(3, 5), (3, 11), (7, 5), (7, 11)} Relation R = {(a, b): a ∈ A, b ∈ B and a + b is even} Roster form R = {(3, 5), (3, 11), (7, 5), (7, 11)} R^-1 = {(5, 3), (11, 3), (5, 7), (11, 7)} Inverse relation R^-1 = {(3, 5), (3, 11), (7, 5), (7, 11)} = A × B Hence relation R^-1 is universal relation

Let A = {3, 7}, B = {5, 11} and relation R = {(a, b): a ∈ A, b ∈ B and a + b is even} then inverse relation R-1 is 1. Identity relation2. Universal relation3. Empty relation4. Both 1 and 2

Answer» Correct Answer - Option 2 : Universal relation

Concept:

If R is a relation from set A to set B, then inverse relation of R to be denoted by R-1, is a relation from set B to set A.

Symbolically R-1 = {(b, a): (a, b) ∈ R for all a ∈ A and b ∈ B}.

A relation R on a set A is said to be identity relation on A if R = {(a, b): a ∈ A, b ∈ A and a = b}.

A relation R from A to B is said to be the universal relation, if R = A ×. B

A relation R from A to B is called an empty relation or a void relation from A to B if R = ø.

Calculation:

Given A = {3, 7}, B = {5, 11}

Cartesian product \(A× B\) = {(3, 5), (3, 11), (7, 5), (7, 11)}

Relation R = {(a, b): a ∈ A, b ∈ B and a + b is even}

Roster form R = {(3, 5), (3, 11), (7, 5), (7, 11)}

R^-1 = {(5, 3), (11, 3), (5, 7), (11, 7)}

Inverse relation R^-1 = {(3, 5), (3, 11), (7, 5), (7, 11)} = A × B

Hence relation R^-1 is universal relation