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.R2 = {(1, 5), (2, 4), (3, 6)}
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)} R₂ = {(1, 5),(2, 4),(3, 6)} Since R₂ ⊆ A × B, R₂ is a relation from A to B. Domain (R₂) = Set of first components of R₂ = {1, 2, 3} Range (R₂ ) = 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.R2 = {(1, 5), (2, 4), (3, 6)}

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)}

R₂ = {(1, 5),(2, 4),(3, 6)}

Since R₂ ⊆ A × B,

R₂ is a relation from A to B.

Domain (R₂) = Set of first components of R₂ = {1, 2, 3}

Range (R₂ ) = Set of second components of R = {4, 5, 6}