Question

Question #af1dd

Answer 1

See below for details.

Explanation:

When relations are defined by a set of paired values,
the first value in each pair is a Domain element
and the second value is a Range element.
We typically say that, for each pair the Domain element "maps into" the Range element.

A relation is a function if no Domain value "maps into" more than one Range value.

For the relations:
`A= {(1, 2); (2, 3); (3, 4); (2, 5)}`

the pairs `(2,3)` and `(2,5)` map the same Domain value (`2`) into different Domain values (`3` and `5`);
therefore `A` is not a function.

`B= {(1, 2); (1, 3); (3, 2); (4, 2)}`

the pairs `(1,2)` and `(1,3)` map the Domain value (`1`) into different Range values;
`B` is not a function.

`C: {(1, 2); (2, 3); (3, 4); (1, 5)}`

the pairs `(1,2)` and `(1,5)` map the Domain value (`1`) into different Range values;
`C` is not a function.

`D= {(1, 2); (2, 5); (3, 2); (4, 5)}`

there are no Domain values which map into more than one Range value;
`D` is a function.

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The Range of the relation `{(1, 2), (2, 4), (3, 2)}`
is the set of Range values, namely `{2,4}` (it is not necessary to include the value `2` in the Range set more than once).