Page "Propositional calculus" Paragraph 26

* Disjunction resembles conjunction in that it forms a proposition out of two simpler propositions.

We write it, and it is read " or ".

It expresses that either or is true.

Thus, in the cases listed above, the disjunction of and is true in all cases except 4.

Using the example above, the disjunction expresses that it is either raining outside or there is a cold front over Kansas.

( Note, this use of disjunction is supposed to resemble the use of the English word " or ".

However, it is most like the English inclusive " or ", which can be used to express the truth of at least one of two propositions.

It is not like the English exclusive " or ", which expresses the truth of exactly one of two propositions.

That is to say, the exclusive " or " is false when both and are true ( case 1 ).

An example of the exclusive or is: You may have a bagel or a pastry, but not both.

Often in natural language, given the appropriate context, the addendum " but not both " is omitted but implied.

In mathematics, however, " or " is always used as inclusive or ; if exclusive or is meant it will be specified, possibly by " xor ".