Jul 17, 2024

- Everyday examples of sets: dinner set, jewelry set, kitchen set.
- Mathematics also deals with sets: well-defined collection of objects.

**Definition of Sets****Set Notation: Roster Form and Set Builder Form****Empty Sets****Finite and Infinite Sets****Equal Sets****Subset and Superset****Singleton Set****Universal Set****Operations on Sets: Union, Intersection, Difference****Complement of a Set****Venn Diagrams**

- Set: a well-defined collection of objects.
- Examples: Rivers of India, students of a school, family members.

- All elements listed, separated by commas, enclosed in braces
`{}`

. - Order does not matter, and no element is repeated.

- Elements are defined by a common property instead of listing.
- Example:
`{x | x is a vowel in the English alphabet}`

.

- Also called null set or void set.
- Represented by
`{}`

or`╬ж`

. - Example: Set of natural numbers between 5 and 6.

- Finite Set: Fixed number of elements.
- Infinite Set: Unlimited number of elements.
- Example: Natural numbers form an infinite set.

- Two sets are equal if they have exactly the same elements.
- Order of elements does not matter.

- Subset: All elements of set A are in set B.
- Superset: Set B contains all elements of set A (and possibly more).

- A set with only one element.

- Contains all possible elements for a particular discussion.
- Example: Set of real numbers can be a universal set containing subsets like rational numbers, integers, etc.

- Denoted by
`A тИк B`

: Combines elements of both sets. - Venn Diagram: Shaded region of both sets combined.

- Denoted by
`A тИй B`

: Common elements in both sets. - Venn Diagram: Shaded overlapping area of both sets.

- Denoted by
`A - B`

: Elements in A but not in B. `B - A`

: Elements in B but not in A.

- Elements not in the set but in the universal set.
- Denoted by
`A'`

.

- Used to depict set operations visually using rectangles (universal sets) and circles (subsets).
- Examples:
- Union of Sets: Combine all elements.
- Intersection of Sets: Common elements.
- Complement: Elements outside the set but within the universal set.

- Examples to illustrate each concept.
- Practice problems to reinforce understanding.

- Commutative, Associative, Identity, and Distributive Laws in Set Operations.

- Practice converting between Roster and Set Builder forms.
- Solve problems using Venn Diagrams for set operations.

- Summary of key points.
- Encouragement to practice with provided problems.
- Announcement of additional resources and upcoming lessons.