<em>The table that shows the relative frequency of data is in the below further explanation.</em>

<h3>Further explanation</h3>
A set is a clearly defined collection of objects.
To declare a set can be done in various ways such as:
- With words or the nature of membership
- By registering its members

Multiplying set A x B is by pairing each member of set A with each member of set B.
<u>Example:</u>
<em>A = {1, 2, 3}</em>
<em>B = {a, b}</em>
Then
A x B = {(1, a), (1, b), (2, a), (2, b), (3, a), (3, b)}

Union of set A and B ( A ∪ B ) is rewriting each member A and combined with each member B.
Intersection of set A and B ( A ∩ B ) is to find the members that are both in Set A and Set B.
<u>Example:</u>
<em>A = {1, 2, 3, 4}</em>
<em>B = {3, 4, 5}</em>
A ∪ B = {1, 2, 3, 4, 5}
A ∩ B = {3, 4}
Let us now tackle the problem!

<em>A sports club has 84 members who learned baseball, and 42 of those members also learned basketball.</em>
![\left[\begin{array}{ccc}&Play Baseball&Don't Play Baseball\\Play Basketball&\boxed{42}& \\Don't Play Basketball& & \end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D%26Play%20Baseball%26Don%27t%20Play%20Baseball%5C%5CPlay%20Basketball%26%5Cboxed%7B42%7D%26%20%5C%5CDon%27t%20Play%20Basketball%26%20%26%20%5Cend%7Barray%7D%5Cright%5D)

Number of members who learned baseball but did not learn basketball will be ( 84 - 42 ) = 42 members
![\left[\begin{array}{ccc}&Play Baseball&Don't Play Baseball\\Play Basketball&42& \\Don't Play Basketball&\boxed{42}& \end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D%26Play%20Baseball%26Don%27t%20Play%20Baseball%5C%5CPlay%20Basketball%2642%26%20%5C%5CDon%27t%20Play%20Basketball%26%5Cboxed%7B42%7D%26%20%5Cend%7Barray%7D%5Cright%5D)

<em>There are 25 students who did not learn baseball but learned basketball</em>
![\left[\begin{array}{ccc}&Play Baseball&Don't Play Baseball\\Play Basketball&42&\boxed{25} \\Don't Play Basketball&42& \end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D%26Play%20Baseball%26Don%27t%20Play%20Baseball%5C%5CPlay%20Basketball%2642%26%5Cboxed%7B25%7D%20%5C%5CDon%27t%20Play%20Basketball%2642%26%20%5Cend%7Barray%7D%5Cright%5D)

<em>8 students did not learn either baseball or basketball</em>
![\left[\begin{array}{ccc}&Play Baseball&Don't Play Baseball\\Play Basketball&42&25 \\Don't Play Basketball&42&\boxed{8} \end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D%26Play%20Baseball%26Don%27t%20Play%20Baseball%5C%5CPlay%20Basketball%2642%2625%20%5C%5CDon%27t%20Play%20Basketball%2642%26%5Cboxed%7B8%7D%20%5Cend%7Barray%7D%5Cright%5D)

<em>Total Number of Students = 42 + 42 + 25 + 8 = 117</em>

Table of relative frequency
![\left[\begin{array}{ccc}&Play Baseball&Don't Play Baseball\\Play Basketball&\boxed{\frac{42}{117}}&\boxed{\frac{25}{117}} \\Don't Play Basketball&\boxed{\frac{42}{117}}&\boxed{\frac{8}{117}} \end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D%26Play%20Baseball%26Don%27t%20Play%20Baseball%5C%5CPlay%20Basketball%26%5Cboxed%7B%5Cfrac%7B42%7D%7B117%7D%7D%26%5Cboxed%7B%5Cfrac%7B25%7D%7B117%7D%7D%20%5C%5CDon%27t%20Play%20Basketball%26%5Cboxed%7B%5Cfrac%7B42%7D%7B117%7D%7D%26%5Cboxed%7B%5Cfrac%7B8%7D%7B117%7D%7D%20%5Cend%7Barray%7D%5Cright%5D)

<h3>Learn more</h3>
<h3>Answer details</h3>
Grade: High School
Subject: Mathematics
Chapter: Sets
Keywords: Sets , Venn , Diagram , Intersection , Union , Mean , Median , Mode