Modus Tollendo Ponens/Sequent Form
Theorem
Case 1
| \(\ds p \lor q\) | \(\) | \(\ds \) | ||||||||||||
| \(\ds \neg p\) | \(\) | \(\ds \) | ||||||||||||
| \(\ds \vdash \ \ \) | \(\ds q\) | \(\) | \(\ds \) |
Case 2
| \(\ds p \lor q\) | \(\) | \(\ds \) | ||||||||||||
| \(\ds \neg q\) | \(\) | \(\ds \) | ||||||||||||
| \(\ds \vdash \ \ \) | \(\ds p\) | \(\) | \(\ds \) |
Also known as
The Modus Tollendo Ponens is also known as the Disjunctive Syllogism, abbreviated D.S.
Sources
- 1973: Irving M. Copi: Symbolic Logic (4th ed.) ... (previous) ... (next): $2$ Arguments Containing Compound Statements: $2.1$: Simple and Compound Statements