Editing Atomic sentence (section)

== Examples ==
=== Assumptions ===
In the following examples:
* let ''F'', ''G'', ''H'' be predicate letters; 
* let ''a'', ''b'', ''c'' be individual constants; 
* let ''x'', ''y'', ''z'' be variables.

=== Atomic sentences ===
These wffs are atomic sentences; they contain no free variables or conjunctions:

* ''F''(''a'')
* ''G''(''a'', ''b'')
* ''H''(''a'', ''b'', ''c'')

=== Atomic formulae ===
These wffs are atomic formulae, but are not sentences (atomic or otherwise) because they include free variables:
* ''F''(''x'')
* ''G''(''a'', ''z'')
* ''H''(''x'', ''y'', ''z'')

=== Compound sentences ===
{{Distinguish|Compound sentence}}
These wffs are compound sentences. They are sentences, but are not atomic sentences because they are not atomic formulae:
* '''∀'''''x'' (''F''(''x''))
* '''∃'''''z'' (''G''(''a'', ''z''))
* '''∃'''''x'' '''∀'''''y'' '''∃'''''z'' (''H''(''x'', ''y'', ''z''))
* '''∀'''''x'' '''∃'''''z'' (''F''(''x'') ∧ ''G''(''a'', ''z''))
* '''∃'''''x'' '''∀'''''y'' '''∃'''''z'' (''G''(''a'', ''z'') ∨ ''H''(''x'', ''y'', ''z''))

=== Compound formulae ===
These wffs are compound formulae. They are not atomic formulae but are built up from atomic formulae using logical connectives. They are also not sentences because they contain free variables:
* ''F''(''x'') ∧ ''G''(''a'', ''z'')
* ''G''(''a'', ''z'') ∨ ''H''(''x'', ''y'', ''z'')