LIVETUTORIALS LEARNING LIBRARY
Deductive Logic and Set Relationships
Represent universal and particular statements precisely, then test whether a conclusion is forced by the premises.
Overview
Deduction is about necessity. If the premises are true, a valid conclusion cannot be false. A conclusion that is merely possible is not enough. This distinction is especially important in statements involving all, none and some, because each word controls what can be inferred.
Set relationships provide a compact representation. Containment expresses “all,” separation expresses “none,” and an explicitly marked overlap expresses “some.” Avoid drawing extra overlaps or extra members unless the premises require them. An attractive diagram can become misleading if it includes assumptions that were never given.
A counterexample is a complete situation that satisfies the premises while violating a proposed conclusion. You only need one counterexample to show that a conclusion does not follow. The syllogism tutorial applies this method to containment, overlap and the common mistake of reversing an all-statement.
Continue learning
- Syllogisms and Counterexamples
Use set containment, separation and explicit existence to test all, none and some statements without adding assumptions.