LIVETUTORIALS LEARNING LIBRARY
Logical Reasoning
Learn to separate assumptions from conclusions and use set diagrams and counterexamples to test deductive arguments.
Overview
A deductive argument asks what must follow from the statements supplied. It does not ask what is common in everyday life or what you expect to happen. Treat the premises as the only information available, and keep outside knowledge separate from the logical question.
One useful method is to rewrite statements using sets. “All A are B” means that the A set is contained within B. “No A are B” means the two sets do not overlap. “Some A are B” asserts that at least one member lies in the overlap. These statements make different commitments, so they cannot be swapped freely.
To test a proposed conclusion, try to draw a situation in which every premise remains true but the conclusion is false. Finding one such counterexample proves that the conclusion is not guaranteed. If no counterexample is possible because the premises force the relationship, the conclusion follows. This discipline helps prevent intuitive but invalid reversals.
Continue learning
- Deductive Logic and Set Relationships
Represent universal and particular statements precisely, then test whether a conclusion is forced by the premises.