I'm trying to construct a truth table in Libreoffice Calc and can't seem too find the implies- nor equivalence functions in the documentation. Do they exist and if so, what are they called?
You could write your own functions. From the menu choose "Tools" -> "Macros" -> "Organize Macros" -> "LibreOffice Basic...". In the new window choose "Tools" -> "Select Module". Create a new module or select and existing and click the "Edit" button. In the code pane you can now define your functions, for example:
Function IMPLIES (A As Boolean, B As Boolean) As Boolean
IMPLIES = (NOT A) OR B
End Function
Function EQUIVALENT (A As Boolean, B As Boolean) As Boolean
EQUIVALENT = (A AND B) OR ((NOT A) AND (NOT B))
End Function
Save and you can use the functions like regular functions in your sheet, e.g. =IMPLIES(TRUE, FALSE)
or =EQUIVALENT(FALSE, TRUE)
.