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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
R1 = {(1, 4), (1, 5), (1, 6)}
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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)}
R1 = {(1, 4), (1, 5), (1, 6)}
Since all the elements of R1 are in A × B,
R1 ⊆ A × B
∴ R1 is the relation from A to B.
Domain of R1 = {1}
Range of R1 = {4, 5, 6}
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