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If A={1,2,3} and B={2,3,4} , find which ...

If A={1,2,3} and B={2,3,4} , find which of the following are the functions from A to B?
(i) `f={(1,2),(2,3),(3,4)}`
(ii) `g={(1,2),(1,3),(2,3),(3,4)}`
(iii) `h={(1,3),(2,4)}`

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To determine which of the given relations are functions from set A to set B, we need to check if each element in set A is related to exactly one element in set B. Given: - Set A = {1, 2, 3} - Set B = {2, 3, 4} We will analyze each relation one by one. ### Step 1: Analyze relation f Relation f = {(1, 2), (2, 3), (3, 4)} - For element 1 in A, it is related to 2 in B. - For element 2 in A, it is related to 3 in B. - For element 3 in A, it is related to 4 in B. Each element of A (1, 2, 3) is related to a unique element in B (2, 3, 4). Therefore, relation f is a function from A to B. ### Step 2: Analyze relation g Relation g = {(1, 2), (1, 3), (2, 3), (3, 4)} - For element 1 in A, it is related to both 2 and 3 in B. - For element 2 in A, it is related to 3 in B. - For element 3 in A, it is related to 4 in B. Here, element 1 in A is related to two different elements in B (2 and 3). Therefore, relation g does not satisfy the definition of a function, as it does not have a unique image for every element of A. Thus, g is not a function from A to B. ### Step 3: Analyze relation h Relation h = {(1, 3), (2, 4)} - For element 1 in A, it is related to 3 in B. - For element 2 in A, it is related to 4 in B. - For element 3 in A, there is no corresponding element in B. Here, element 3 in A does not have any relation in B. Since not every element in A is related to an element in B, relation h is not a function from A to B. ### Conclusion - Relation f is a function from A to B. - Relation g is not a function from A to B. - Relation h is not a function from A to B.
To determine which of the given relations are functions from set A to set B, we need to check if each element in set A is related to exactly one element in set B. Given: - Set A = {1, 2, 3} - Set B = {2, 3, 4} We will analyze each relation one by one. ...
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