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SETS - Coggle Diagram
SETS
Definition
A set is a well-defined collection of distinct objects.
Notation: A = {1, 2, 3}
Example: Fruits = {apple, banana, mango}
Types of Sets
Finite Set
Countable number of elements
Example: A = {2, 4, 6}
Infinite Set
Uncountable number of elements
Example: Natural Numbers = {1, 2, 3, ...}
Empty Set (Null Set)
Set with no elements
Symbol: ∅ or { }
Singleton Set
A set with exactly one element
Example: B = {5}
Equal Sets
Two sets with same elements
Example: A = {a, b}, B = {b, a}
Subset
A ⊆ B means all elements of A are in B
Example: A = {1,2}, B = {1,2,3}
Power Set
Set of all subsets
If A = {1,2} → P(A) = {∅, {1}, {2}, {1,2}}
Universal Set
Contains all elements under discussion
Example: U = {1,2,3,4,5}
Set Operations
Union (A ∪ B)
Combines all elements of A and B (no duplicates)
Example: A = {1,2,3}, B = {3,4,5} → A ∪ B = {1,2,3,4,5}
Real-life: People who like either iOS or Android
Intersection (A ∩ B)
Common elements between A and B
Example: A = {red, blue}, B = {blue, green} → A ∩ B = {blue}
Real-life: Students taking both Math and Science
Difference (A − B)
Elements in A not in B
Example: A = {a, b, c}, B = {b} → A − B = {a, c}
Real-life: Friends invited but didn't attend the party
Complement (A′)
Elements in universal set but not in A
U = {1,2,3,4,5}, A = {2,4} → A′ = {1,3,5}
Real-life: People not attending the event
Major Set Laws
Commutative Law
A ∪ B = B ∪ A
A ∩ B = B ∩ A
Real-life: Merging contact lists in any order
Associative Law
(A ∪ B) ∪ C = A ∪ (B ∪ C)
(A ∩ B) ∩ C = A ∩ (B ∩ C)
Real-life: Grouping TV subscriptions - Netflix, Prime, Disney+
Distributive Law
A ∩ (B ∪ C) = (A ∩ B) ∪ (A ∩ C)
A ∪ (B ∩ C) = (A ∪ B) ∩ (A ∪ C)
Real-life: Applying filters across multiple apps
De Morgan's Laws
(A ∪ B)' = A' ∩ B'
(A ∩ B)' = A' ∪ B'
Real-life: Not liking tea or coffee = liking neither