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The symbol '¬' represents negation, meaning 'not'. For example, if p is 'It is raining', ¬p translates to 'It is not raining'.

The symbol '↔' represents a biconditional, meaning 'if and only if'. For example, if p is 'It is raining' and q is 'The ground is wet', p ↔ q translates to 'The ground is wet if and only if it is raining'.

The symbol '→' represents a conditional, or 'implies'. For example, if p is 'It is raining', and q is 'The ground is wet', p → q translates to 'If it is raining, then the ground is wet'.

The symbol '∨' represents disjunction, meaning 'or'. For example, if p is 'It is raining' and q is 'It is cold', p ∨ q translates to 'It is raining or it is cold' (inclusive).

The symbol '∀' represents universal quantification, it stands for 'for all'. For example, if p(x) is 'x is blue', ∀x p(x) translates to 'Everything is blue'.

The symbol '∃' represents existential quantification, meaning 'there exists'. For example, if p(x) is 'x is blue', ∃x p(x) translates to 'There exists something that is blue'.

The symbol '∧' represents conjunction, meaning 'and'. For example, if p is 'It is raining' and q is 'It is cold', p ∧ q translates to 'It is raining and it is cold'.