Logical Deduction Guides
Patterns of valid reasoning including syllogisms and propositional logic Solving constraint-based logic puzzles including seating arrangements, group assignments, and ordering sequences
Barbara Syllogism
The most fundamental valid syllogism: All A are B, All B are C, therefore All A are C.
View Guides →Celarent Syllogism
A valid syllogism with negative conclusion: No A are B, All C are A, therefore No C are B.
View Guides →Darii Syllogism
A valid syllogism with particular conclusion: All A are B, Some C are A, therefore Some C are B.
View Guides →Ferio Syllogism
A valid syllogism: No A are B, Some C are A, therefore Some C are not B.
View Guides →Modus Ponens
The 'affirming mode': If P then Q, P is true, therefore Q is true.
View Guides →Modus Tollens
The 'denying mode': If P then Q, Q is false, therefore P is false.
View Guides →Hypothetical Syllogism
Chain reasoning: If A then B, If B then C, therefore If A then C.
View Guides →Disjunctive Syllogism
Either/Or reasoning: Either A or B, not A, therefore B.
View Guides →Contrapositive
Logical equivalence: 'If A then B' is equivalent to 'If not B then not A'.
View Guides →Transitive Relation
If A > B and B > C, then A > C. Applies to ordering relations.
View Guides →Biconditional
'A if and only if B' means A and B are either both true or both false.
View Guides →Seating Arrangement
Determining positions of people in a row based on constraint clues like adjacency, relative order, and fixed positions.
View Guides →Group Assignment
Assigning items or people to groups under same-team, different-team, and fixed-group constraints.
View Guides →Ordering Sequence
Determining the rank order of items from comparison clues like higher-than, lower-than, and not-at-rank constraints.
View Guides →Enthymeme
A syllogism in which one premise (or sometimes the conclusion) is left unstated and must be supplied by the reader.
View Guides →Sorites (Chained Syllogism)
A polysyllogism where the conclusion of each syllogism becomes a premise of the next, linking multiple premises to a single final conclusion.
View Guides →Truth Table
A table listing every possible truth-value combination of input propositions and the resulting truth value of a compound formula.
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