A rule of inference in Propositional logic. Disjunctive Syllogism is also called modus tollendo ponens. It is used to break up a disjunctive statement, like this:

Therefore, Q

I have an apple or an orange.
I don't have an apple.
Therefore, I have an orange.

Note that in this case 'or' (∨) is used in the nonexclusive sense of or, AKA and/or. That is to say, "I have an apple or an orange" is true even if you have an an apple AND an orange.

Abbreviated as DS.

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