

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 
Contrapositive The Contrapositive is a rule of inference pertaining to the IF/THEN operator. The Contrapositive states that in a conditional, if the consequent is false, then the antecedent must be false also. 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. If we apply the Contrapositive to this expression, we would obtain the following: "If there are no clouds in the sky, then it is not raining." This makes perfect sense. Let's write our steps formally: p > q: "If it is raining, then there are clouds in
the sky." The original conditional is above the line of dashes, and the new expression ~q > ~p formed by applying the Contrapositive is below the line.
Other examples of the Contrapositive R > W: "If the light is off, then it is dark."
S > W: "If there is snow, then it is wintertime."
Links to Relevant Problems These are links to validity proof problems whose solutions contain the Contrapositive.
