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If A = {3, 5, 7, 9} and B = {a, b, c}, t...

If A = {3, 5, 7, 9} and B = {a, b, c}, then which of the following are relations from A to B ? Give reasons for your answer.
(i) `R_(1) = {(3, a), (5, b), (5, c)}`
(ii) `R_(2) = {(3, c), (9, b), (5, a)}`
(iii) `R_(3) = {(3, c), (b, c), (7, b), (9, a)}`
(iv) `R_(4) = {(3, b), (7, c), (c, a), (b, 9)}`

Text Solution

AI Generated Solution

To determine which of the given sets are relations from set A to set B, we first need to understand what a relation from A to B is. A relation from set A to set B is defined as a subset of the Cartesian product A × B, which consists of all possible ordered pairs (a, b) where a ∈ A and b ∈ B. Given: - Set A = {3, 5, 7, 9} - Set B = {a, b, c} **Step 1: Calculate the Cartesian Product A × B** ...
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