We have developed the logic of propositions using only three basic notions cor- responding (perhaps roughly) to the English words “and,” “or,” and “not.” Now let us go back to the question of the two possible senses of the word “or“: one exclusive and the other inclusive. Sometimes “or” seems to rule out the possibility that both alternatives are true; at other times “or” seems to allow this possibility. This is the difference between exclusive and inclusive disjunction.
Suppose we use the symbol “ ” to stand for exclusive disjunction. This is the same as the symbol for inclusive disjunction except that it is underlined. (After this discussion, we will not use it again.) We could then give two truth table definitions, one for each of these symbols:
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