# Which relation is a function? A. {(1, 2); (2, 3); (3, 4); (2, 5)} B. {(1, 2); (1, 3); (3, 2); (4, 2)} C. {(1, 2); (2, 3); (3, 4); (1, 5)} D. {(1, 2); (2, 5); (3, 2); (4, 5)} What is the range of the relation? {(1, 2), (2, 4), (3, 2),

##### 1 Answer

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#### Explanation

#### Explanation:

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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:

the pairs

#(2,3)# and#(2,5)# map the same Domain value (#2# ) into different Domain values (#3# and#5# );

therefore#A# isnota function.

the pairs

#(1,2)# and#(1,3)# map the Domain value (#1# ) into different Range values;

#B# isnota function.

the pairs

#(1,2)# and#(1,5)# map the Domain value (#1# ) into different Range values;

#C# isnota function.

there are no Domain values which map into more than one Range value;

#D# isa function.

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The Range of the relation

is the set of Range values, namely

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