Inference: Disjunctive and Hypothetical Syllogism

Disjunctive syllogism

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

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

Examples

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