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Universal Quantification; '∀x: P(x)' means 'P(x) is true for all x'.

Logical OR; The statement 'p ∨ q' is true if either 'p' or 'q' (or both) are true.

Material Implication; 'p → q' is false only if 'p' is true and 'q' is false.

Bi-conditional; 'p ↔ q' is true when 'p' and 'q' have the same truth values.

Negation; '¬p' is true if 'p' is false, and vice versa.

Null Set; The symbol '∅' represents an empty set, a set with no elements.

Logical AND; The statement 'p ∧ q' is true if both 'p' and 'q' are true.

Existential Quantification; '∃x: P(x)' means 'There exists an x such that P(x) is true'.

Union; 'A ∪ B' denotes a set containing all elements that are in set 'A', in set 'B', or in both.

Intersection; 'A ∩ B' denotes a set containing all elements that are both in set 'A' and in set 'B'.

Element of; 'a ∈ S' means that 'a' is an element of the set 'S'.