Question

The 5-tuples in a 5-ary relation represent these attributes of all people in the United States: name, Social Security number, street address, city, state.

a) Determine a primary key for this relation.

b) Under what conditions would (name, street address) be a composite key?

c) Under what conditions would (name, street address, city) be a composite key?

Short answer

(a) Social security number.

(b) No 2 people with the same name live at the same street address.

(c) No 2 people with the same name live at the same street address in the same city.

Step-by-step solution

Given data

5-tuples in a 5-ary is given.

Concept of sets

The concept of set is a very basic one. It is simple; yet, it suffices as the basis on which all abstract notions in mathematics can be built.\(A\)set is determined by its elements. If\(A\)is a set, write\(x \in A\)to say that\(x\)is an element of\(A\).

Simplify the expression

(a)

A primary key is a domain that has a unique value for each \(n\)-tuple.

Name is not likely to be a primary key, because there are different people with the same name (such as John Doe).

Social security number is likely a primary key, because each person tends to be assigned a unique Social Security number.

Street address is not likely to be a primary key, because it multiple people can live at the same street address (such as siblings, husbands/wives).

City is not likely to be a primary key, because multiple people live in each city.

State is not likely to be a primary key, because multiple people live in each state.

Simplify the expression

(b)

A composite key is a collection of domains that has a unique value for each \(n\)-tuple. Name and street address are a composite key, when no 2 people with the same name live at the same street address.

Simplify the expression

(c)

A composite key is a collection of domains that has a unique value for each \(n\)-tuple. Name, Street address and City are a composite key, when no 2 people with the same name live at the same street address in the same city.

In practice, this is very likely to occur.