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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.
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