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.R4 = {(4, 2), (2, 6), (5, 1), (2, 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)} R₄ = {(4, 2), (2, 6), (5, 1), (2, 4)} Since (4, 2) ∈ R₄ , but (4, 2) ∉ A × B, R₄ ⊄ A × B ∴ R₄ is not a relation from A to B.

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.R4 = {(4, 2), (2, 6), (5, 1), (2, 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)}

R₄ = {(4, 2), (2, 6), (5, 1), (2, 4)}

Since (4, 2) ∈ R₄ , but (4, 2) ∉ A × B, R₄ ⊄ A × B

∴ R₄ is not a relation from A to B.