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Found in: Page 590

### Discrete Mathematics and its Applications

Book edition 7th
Author(s) Kenneth H. Rosen
Pages 808 pages
ISBN 9780073383095

# 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?

(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.

See the step by step solution

## Step 1: Given data

5-tuples in a 5-ary is given.

## Step 2: 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 $$A$$.

## Step 3: 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.

## Step 4: 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.

## Step 5: 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.