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Give an example of a relation with the following characteristics:
The relation is a function containing 2 ordered pairs. Reversing the components in each ordered
pair results in a relation that is not a function. Explain why your example works.
Solution
Such a relation is {(2,5);(3,5)}.
This is a function.
But on on reversing the components of ordered pairs we get a relation as:
{(5,2);(5,3)} which is not a function.
This is because for a relation to be a function,there is assigned exactly one element of the range
to each element of the domain which is violated here[both 2 and 3 of the range being assigned to
one element of domain, i.e.5]

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Give an example of a relation with the following characteristicsT.pdf

  • 1. Give an example of a relation with the following characteristics: The relation is a function containing 2 ordered pairs. Reversing the components in each ordered pair results in a relation that is not a function. Explain why your example works. Solution Such a relation is {(2,5);(3,5)}. This is a function. But on on reversing the components of ordered pairs we get a relation as: {(5,2);(5,3)} which is not a function. This is because for a relation to be a function,there is assigned exactly one element of the range to each element of the domain which is violated here[both 2 and 3 of the range being assigned to one element of domain, i.e.5]