Databases

Problem 01

Basics of Sets and Relations 01

You are given two sets:

• \(Set\, A = \{1,2,3,4,5,6\}\)
• \(Set\, B = \{2,3,4,5,6,7,8\}\)

How many elements are present in \(A \cup B\) ?

Solution

\(A \cup B = 8 = \{1,2,3,4,5,6,7,8\}\)

Problem 02

Basics of Sets and Relations 02

You are given two sets:

• \(Set\, A = \{1,2,3,4,5,6\}\)
• \(Set\, B = \{2,3,4,5,6,7,8\}\)

How many elements are present in \(A \cap B\) ?

Solution

\(A \cap B = 5 = \{2,3,4,5,6\}\)

Problem 03

Basics of Sets and Relations 03

You are given two sets:

• \(Set\, A = \{1,2,3,4,5,6\}\)
• \(Set\, B = \{2,3,4,5,6,7,8\}\)

How many elements are present in \(A - B\) ?

Solution

\(A - B = 1 = \{1\}\)

Problem 04

Basics of Sets and Relations 04

You are given two sets:

• \(Set\, A = \{1,2,3,4,5,6\}\)
• \(Set\, B = \{2,3,4,5,6,7,8\}\)

What is the total number of ordered pairs present in the Cartesian Product \(A \times B\)

Solution

\(A \times B = 6 \cdot 7 = 42 = \{(1,2),(1,3),...,(2,2),(2,3),...,(6,7),(6,8)\}\)

Problem 05

Basics of Sets and Relations 05

Consider the following data table named Student

Student Name	Number	Sex
Ben	3412	M
Dan	1234	M
Nel	2341	F

What is the count of rows returned in the following relational selection:

\[\begin{align} \sigma(Number < 3000)(Student) \end{align}\]

Solution

\(\sigma(Number < 3000)(Student) = 2 = \{1234,2341\}\)