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The disjunction operator ∨ represents 'or'. A compound proposition p ∨ q is true if either p or q is true (inclusive).

The contradiction symbol ⊥ represents a proposition that is always false, regardless of the truth values of its components.

The negation operator ¬ negates the truth value of a proposition. If a proposition p is true, ¬p is false; if p is false, ¬p is true.

The conjunction operator ∧ represents 'and'. A compound proposition p ∧ q is true only if both p and q are true.

The exclusive or operator ⊕ represents 'either...or' (but not both). A compound proposition p ⊕ q is true when either p or q is true, but not both.

The biconditional operator ↔ represents 'if and only if'. A compound proposition p ↔ q is true if both p and q have the same truth value.

The universal quantification operator ∀ denotes 'for all'. It asserts that a predicate holds for all members of a specified set.

The existential quantification operator ∃ denotes 'there exists'. It asserts that there is at least one element in a set for which the predicate holds.

The tautology symbol ⊤ represents a proposition that is always true, regardless of the truth values of its components.