Set operations

A set is a well-defined collection of distinct elements.

Union

The union of two sets A and B is a new set containing all the elements present in either set A, B or both. It is represented as:

Example

 If set $A = \{1, 2, 3, 4\}$ and $B = \{6, 7\}$

Then, $A \cup B = \{1, 2, 3, 4, 6, 7\}$

Intersection

The intersection of two sets A and B is a set that contains all the elements common to both set A and set B.

It is represented as

Example

 If set $A = \{1, 2, 3, 4\}$ and $B = \{1, 2, 5\}$

Then, $A \cap B = \{1, 2\}$

Difference

The difference between two sets A and B is a set that contains all the elements of set A that are not present in set B.

It is represented as

Example

 If set $A = \{1, 2, 3, 4\}$ and $B = \{2, 4, 6\}$

Then, $A - B = \{1, 3\}$

Complement

The complement of a set A is a set that contains all the elements that are not present in set A but exist in the universal set $U$.

It is represented as

Example

 If set $U = \{1, 2, 3, 4, 5\}$ and $A = \{1, 2, 4, 6\}$

Then, $A' = \{3, 5\}$

Cartesian product

Given two sets A and B, the cartesian product is the set of all possible ordered pairs $(a, b)$, where $a$ is an element of set A, and $b$ is an element of set B. It is represented as

Example

 If set $A = \{1, 2, 3\}$ and $B = \{3, 5\}$

Then, $A \times B= \{(1,3), (1,5), (2,3) , (2,5), (3,3), (3,5)\}$

Conclusion

Set operations are fundamental mathematical concepts that allow us to combine, compare, and manipulate sets, providing valuable data organization and analysis tools.