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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

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(i) Since 4, 5, 6 are the elements of domain of R having their unique images, this relation R is a function.
(ii) Since the same first element 2 corresponds to two different images 3 and 5, this relation is not a function.
(iii) Since every element has one and only one image, this relation is a function.
(iv) Since every element has one and only one image, this relation is a function.
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