Sets and Symbols

Introduction to Sets

Common Universal Sets

Other Notations

e is an element of S is written expressed as: e∈S. e is not an elements of S is written as: e∉S.


Set Operations

Definition: Two sets P and Q are equal, denoted P = Q, iff
∀x [x∈P↔x∈Q]
The symbol ↔ means logically equivalent (and also the statement is true if both parts are true, or both are false).
It is also important to note that the previous statement is also the same as:
P = Q iff ∀x [(x∈P→x∈Q) ∧ (x∈Q → x∈Q)]
P = Q iff P ⊆ Q and Q ⊆ P

Intersection, Union, and Complement

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Date of last modification: 2024