Reazyn — Play

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Deductive Logic

If the premises are true, the conclusion must be true. Certainty through structure.

7 topics · 17 rules ▼

∧ Conjunction 2 rules ▼

Conjunction Introduction P is true. Q is true. Therefore P and Q. ● Live Conjunction Elimination P and Q are true. Therefore P (or Q) alone is true. ● Live

¬ Negation 2 rules ▼

Double Negation Not-not-P is equivalent to P. Coming Soon Reductio ad Absurdum Assuming P leads to contradiction, so P must be false. Coming Soon

∨ Disjunction 2 rules ▼

Disjunctive Syllogism P or Q. Not P. Therefore Q. Coming Soon Disjunction Introduction P is true. Therefore P or Q must be true. Coming Soon

( ) Grouping 3 rules ▼

Association Regrouping terms within conjunctions or disjunctions. Coming Soon Commutativity Order of terms in a conjunction or disjunction doesn't change truth. Coming Soon Distribution Expanding a conjunction across a disjunction or vice versa. Coming Soon

T/F Truth-Functions 3 rules ▼

Truth Table Construction Map all possible truth values of a compound statement. Coming Soon Tautology Recognition Identify statements that are true under all interpretations. Coming Soon Contradiction Recognition Identify statements that are false under all interpretations. Coming Soon

→ Conditional 4 rules ▼

Modus Ponens If P then Q. P is true. Therefore Q. ● Live Modus Tollens If P then Q. Q is false. Therefore P is false. Coming Soon Hypothetical Syllogism If P then Q. If Q then R. Therefore if P then R. Coming Soon Exportation If P and Q then R, is equivalent to if P then if Q then R. Coming Soon

↔ Biconditional 3 rules ▼

Biconditional Introduction If P then Q, and if Q then P. Therefore P if and only if Q. Coming Soon Biconditional Elimination P ↔ Q means both P→Q and Q→P hold simultaneously. Coming Soon Equivalence Two statements with identical truth values under all conditions. Coming Soon

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Inductive Logic

Patterns and evidence support probable conclusions. Strong but not certain.

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Abductive Logic

Reason to the best available explanation given incomplete information.

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Biases & Fallacies

Recognize the patterns that distort reasoning — in others and in yourself.

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Critical Thinking

Applied reasoning across complex, real-world scenarios. Game modes instead of rules.

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Abstract Thinking

Reason with concepts detached from concrete examples. The highest form of pattern recognition.

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Strategic Thinking

Reason across time, competing interests, and uncertain outcomes toward a long-term goal.

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Metacognitive Thinking

Reason about your own reasoning. Know when you are thinking well — and when you are not.

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Mental Models

Apply frameworks from across disciplines to understand how systems, people, and ideas behave.

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Train your mind toreason clearly.

Train your mind to
reason clearly.