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Found in: Page 589

### Discrete Mathematics and its Applications

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

# Assuming that no new $$n$$-tuples are added, find all the primary keys for the relations displayed ina) Table 3b) Table 5 c) Table 6d) Table 8

(a) The resultant answer is Course.

(b) The resultant answer is Course number.

(c) The resultant answer is Course number.

(d) The resultant answer is Departure time.

See the step by step solution

## Step 1: Given data

Table 3,5,6,8 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. In table 3, we note that student is not a primary key, because Glauser, Marcus and Miller are mentioned more than once in the table. In table 3, we note that major is not a primary key, because Biology, Mathematics and Computer Science are mentioned more than once in the table.

In table 3, we note that course is a primary key, because the course in each row of the table is different.

## Step 4: Simplify the expression

(b)

In table 5, we note that professor is not a primary key, because Cruz, Farber, grammer and Rosen are mentioned more than once in the table.

In table 5, we note that Department is not a primary key, because Zoology, Psychology and Physics are mentioned more than once in the table. In table 5, we note that Course number is a primary key, because the course number in each row of the table is different.

## Step 5: Simplify the expression

(c)

In table 6, we note that Department is not a primary key, because Mathematics, Psychology and Zoology are mentioned more than once in the table.

In table 6, we note that Course number is a primary key, because the course number in each row of the table is different.

In table 6, we note that Room is not a primary key, because N52l and Al00 are mentioned more than once in the table.

In table 6, we note that Time is not a primary key, because 3:00 P.M. and 4:00 P.M. are mentioned more than once in the table.

## Step 6: Simplify the expression

(d)

In table 8, we note that Airline is not a primary key, because Nadir and Acme are mentioned more than once in the table.

In table 8, we note that Flight number is not a primary key, because 122 is mentioned more than once in the table. In table 8, we note that Gate is not a primary key, because 34 and 22 are mentioned more than once in the table.

In table 8, we note that Destination is not a primary key, because Detroit and Denver are mentioned more than once in the table. In table 8, we note that Departure time is a primary key, because the departure time in each row of the table is different.