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Lemma: Disjunctive Syllogism

The disjunctive syllogism is a valid logical argument consisting of two premises and a conclusion, which altogether are constructed from two propositions $p$ and $q$ as follows:

• The first premise (called the major premise) is the disjunction $p\vee q$.
• The second premise (called the minor premise) is the negated proposition $\neg p$.
• The proposition $q$ is the conclusion of the disjunctive syllogism.

Formally,the disjunctive syllogism is the following logical argument: $$\begin{array}{rll} p\vee q&\text{major premise}&\text{e.g. Either it is raining or the sun is shining (or both).}\\ \neg p&\text{minor premise}&\text{e.g. It is not raining.}\\ \hline q&\text{conclusion}&\text{e.g. Therefore, the sun is shining.}\\ \end{array} $$

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References

Bibliography

1. Kane, Jonathan: "Writing Proofs in Analysis", Springer, 2016