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Examine each of the following relations...

Examine each of the following relations given below and state in each case, giving reasons whether it is a function or not ?
(i) `R={(4,1),(5,1),(6,7)}`
(ii) `R={(2,3),(2,5),(3,3),(6,6)}`
(iii) `R={(1,2),(2,3),(3,4),(4,5),(5,6),(6,7)}`
(iv) `R={(1,1),(2,1),(3,1),(4,1),(5,1)}`

Text Solution

AI Generated Solution

To determine whether each of the given relations is a function, we need to check if every input (first element of each ordered pair) is associated with exactly one output (second element of each ordered pair). If any input is associated with more than one output, then the relation is not a function. Let's analyze each relation step by step: ### (i) R = {(4, 1), (5, 1), (6, 7)} 1. **Identify the inputs (x-values)**: - The x-values are 4, 5, and 6. ...
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