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Q9E

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Discrete Mathematics and its Applications
Found in: Page 590
Discrete Mathematics and its Applications

Discrete Mathematics and its Applications

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

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Short Answer

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 by Step Solution

TABLE OF CONTENTS :
TABLE OF CONTENTS

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.

Most popular questions for Math Textbooks

(a) To find Relation\({R^2}\)

(b) To find Relation \({R^3}\)

(c) To find Relation \({R^4}\)

(d) To find Relation\({R^5}\)

Let \(R\)be the relation on the set of people consisting of pairs \((a,b)\), where \(a\) is a parent of \(b\). Let \(S\) be the relation on the set of people consisting of pairs \((a,b)\), where \(a\) and \(b\)are siblings (brothers or sisters). What are \(S^\circ R\) and \(R^\circ S\)?

List the triples in the relation\(\{ (a,b,c)|a,b\;{\bf{and}}\;\;c\,{\bf{are}}{\rm{ }}{\bf{integers}}{\rm{ }}{\bf{with}}\;0 < a < b < c < 5\} \).

An example of a relation on a set that is neither symmetric and anti symmetric.

Exercises 34–37 deal with these relations on the set of real numbers:

\({R_1} = \left\{ {\left( {a,\;b} \right) \in {R^2}|a > b} \right\},\) the “greater than” relation,

\({R_2} = \left\{ {\left( {a,\;b} \right) \in {R^2}|a \ge b} \right\},\) the “greater than or equal to” relation,

\({R_3} = \left\{ {\left( {a,\;b} \right) \in {R^2}|a < b} \right\},\) the “less than” relation,

\({R_4} = \left\{ {\left( {a,\;b} \right) \in {R^2}|a \le b} \right\},\) the “less than or equal to” relation,

\({R_5} = \left\{ {\left( {a,\;b} \right) \in {R^2}|a = b} \right\},\) the “equal to” relation,

\({R_6} = \left\{ {\left( {a,\;b} \right) \in {R^2}|a \ne b} \right\},\) the “unequal to” relation.

34. Find

(a) \({R_1} \cup {R_3}\).

(b) \({R_1} \cup {R_5}\).

(c) \({R_2} \cap {R_4}\).

(d) \({R_3} \cap {R_5}\).

(e) \({R_1} - {R_2}\).

(f) \({R_2} - {R_1}\).

(g) \({R_1} \oplus {R_3}\).

(h) \({R_2} \oplus {R_4}\).
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