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Truth-functional Connectives

A \emph{connective} joins zero or more sentences to make a new sentence. Examples of connectives include: `∧', `¬', `$\bot$' and `because'.
A sentence joined by a connective is a \emph{constituent}. For example, consider the sentence ‘P because Q’: P is a constituent of this sentence.
A \emph{truth functional connective} produces a new sentence whose truth value depends only on the truth values of its constituent sentences.
When P and Q are both true, ‘P because Q’ is sometimes true and sometimes false. Therefore, ‘because’ is not a truth functional connective. To illustrate, consider `Alan got yellow cards because some apples are green' and `Alan got yellow cards because he used his elbows'. All the constituent sentences are true, but the first sentence is false whereas the second is true.