

Sample sentences AND operator IF/THEN operator NOT operator OR operator XOR operator Chain Rule Conjunctive Addition Contrapositive DeMorgan's Law Disjunctive Addition Disjunctive Inference Disjunctive Infer. (XOR) Double Negation Modus Ponens Modus Tollens Mutual Exclusion Simplification 2step 3step 4step 5step or more Bad Argument 
Modus Tollens Modus Tollens is a rule of inference pertaining to the IF/THEN operator. Modus Tollens states that if the consequent of a conditional is false, then the antecedent must also be false. Imagine we have the following conditional sentence: "If it is raining, then there are clouds in the sky." Formally, we would write: p > q: "If it is raining, then there are clouds in
the sky." In this expression, "If it is raining" is the antecedent and "There are clouds in the sky" is the consequent. Now if we know for a fact that there are no clouds in the sky, we can safely conclude that it is not raining. If the consequent ("There are clouds in the sky") is false, then the antecedent ("It is raining") must also be false, by Modus Tollens. Let's write our steps formally: p > q: "If it is raining, then there are clouds in
the sky." The conditional p > q and the given ~q are above the line of dashes, and the conclusion ~p obtained by applying Modus Tollens is below the line.
Other examples of Modus Tollens M > C: If you get enough money, you can buy a new car.
S > F: If there is smoke, there is a fire.
Links to Relevant Problems These are links to validity proof problems whose solutions contain Modus Tollens. 2step problem (A)
