If A = {1, 2, 3}, B = {4, 5, 6}, check if the following are relations

1.	If A = {1, 2, 3}, B = {4, 5, 6}, check if the following are relations from A to B. Also, write its domain and range.R3 = {(1, 4), (1, 5), (3, 6), (2, 6), (3, 4)}
Answer» A = {1, 2, 3}, B = {4, 5, 6} ∴ A × B = {(1, 4), (1, 5), (1, 6), (2,4), (2, 5), (2, 6), (3, 4), (3, 5), (3, 6)} R₃ = {(1, 4), (1, 5), (3, 6), (2, 6), (3, 4)} Since R₃ ⊆ A × B, R is a relation from A to B. Domain (R₃) = Set of first components of R = {1, 2, 3} Range (R₃) = Set of second components of R = {4, 5, 6}

If A = {1, 2, 3}, B = {4, 5, 6}, check if the following are relations from A to B. Also, write its domain and range.R3 = {(1, 4), (1, 5), (3, 6), (2, 6), (3, 4)}

Answer»

A = {1, 2, 3}, B = {4, 5, 6}

∴ A × B = {(1, 4), (1, 5), (1, 6), (2,4), (2, 5), (2, 6), (3, 4), (3, 5), (3, 6)}

R₃ = {(1, 4), (1, 5), (3, 6), (2, 6), (3, 4)}

Since R₃ ⊆ A × B, R is a relation from A to B.

Domain (R₃) = Set of first components of R = {1, 2, 3}

Range (R₃) = Set of second components of R = {4, 5, 6}