<Dd> "Mary believes that the moon is made of green cheese" </Dd> <P> is false . In both cases, each component sentence (i.e. "Al Gore was president of the USA on April 20, 2000" and "the moon is made of green cheese") is false, but each compound sentence formed by prefixing the phrase "Mary believes that" differs in truth - value . That is, the truth - value of a sentence of the form "Mary believes that ..." is not determined solely by the truth - value of its component sentence, and hence the (unary) connective (or simply operator since it is unary) is non-truth - functional . </P> <P> The class of classical logic connectives (e.g. &, →) used in the construction of formulas is truth - functional . Their values for various truth - values as argument are usually given by truth tables . Truth - functional propositional calculus is a formal system whose formulae may be interpreted as either true or false . </P> <P> In two - valued logic, there are sixteen possible truth functions, also called Boolean functions, of two inputs P and Q. Any of these functions corresponds to a truth table of a certain logical connective in classical logic, including several degenerate cases such as a function not depending on one or both of its arguments . Truth and falsehood is denoted as 1 and 0 in the following truth tables, respectively, for sake of brevity . </P>

When does a compound sentence become non-truth-functional answer it as elaborately as you can