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Consider the two groups listed below. Which statement describes the sets?

house
complete mailing address

The relation (house, complete mailing address) is a function, but the relation (complete mailing address, house) is not.
The relation (complete mailing address, house) is a function, but the relation (house, complete mailing address) is not.
Both (house, complete mailing address) and (complete mailing address, house) are functions.
Neither the relation (house, complete mailing address) nor the relation (complete mailing address, house) is a function.

1 Answer

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Final answer:

The relationship where each house is associated with exactly one complete mailing address is a function, but one complete mailing address may correspond to multiple houses, so the inverse is not a function.

Step-by-step explanation:

In mathematics, a function describes a specific kind of relationship between two sets, where each member of the first set is associated with exactly one member of the second set. When we consider the relationship between a house and a complete mailing address, it is reasonable to say that each house has exactly one complete mailing address, thus making the relation (house, complete mailing address) a function. On the other hand, it is possible for different houses to have the same mailing address (such as in the case of apartment units), meaning that the relation (complete mailing address, house) could associate one mailing address with multiple houses, therefore, it is not a function.

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