DISCRETE MATHEMATICS (UNIT 1)

Unit 1: Set Theory & Venn Diagrams

Universal Set (U)

The set containing all objects or elements under consideration.

Null Set / Empty Set (∅ or {})

A set which contains no elements.

Subset

Every element in set A is also found in set B.

Power Set

The set containing all possible subsets of a set. A set with n elements has exactly 2 n subsets.

Union (A ∪ B)

The set of elements that are in A, or in B, or in both.

Intersection (A ∩ B)

The set of elements that are strictly in both A and B.

Disjoint Sets

Two sets are disjoint if their intersection is empty (A ∩ B = ∅).

Difference (A − B or A \ B)

The set of elements in A that are not in B.

Symmetric Difference (A ⊕ B)

Elements that are in A or in B, but not in both. (A ∪ B) − (A ∩ B).

Cartesian Product (A × B)

The set of all ordered pairs (a, b) where a ∈ A and b ∈ B.

Identity Laws

Domination Laws

Idempotent Laws

De Morgan’s Laws

Absorption Laws