Inference: Disjunctive and Hypothetical Syllogism

Learn about disjunctive and hypothetical syllogism.

Disjunctive syllogism

If we know that (q1q2)\left(q_1 \lor q_2\right) is true and further we know that ¬q1\neg q_1 is true, then we can conclude that q2q_2 is true. We can write it as the following tautology:

(q1q2)¬q1q2.\left(q_1 \lor q_2\right)\land \neg q_1\Rightarrow q_2.


To further comprehend the application of this rule, let’s look at a few examples.

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