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Question
Answer the following:
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)}
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Solution
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 all the elements of R3 are in A × B, R3 ⊆ A × B
∴ R3 is the relation from A to B.
Domain of R3 = {1, 2, 3}
Range of R3 = {4, 5, 6}
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