

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 
Validity Proof Problems (3 steps) The problems below can be solved in three steps.
Problem 1 1. C > ~(D v E) We have a conditional in premise 1 and its antecedent in premise 2. This immediately prompts us to use Modus Ponens. 3. ~(D v E) 1,2 Modus Ponens Now we can apply DeMorgan's Law to this new expression. 4. ~D ^ ~E 3 DeMorgan's Law We have to prove that ~D is true, and we see that ~D is part of the conjunction in step 4. We can apply Simplification to separate it out. 5. ~D 4 Simplification We have gotten to the conclusion. 1. C > ~(D v E)
Problem 2 1. A > B We can easily separate C out of premise 3 using Simplification. We could do so with D as well, but we are not going to need it anywhere. 4. C 3 Simplification Premise 2 has an exclusive disjunction, and we have just proved that one of its disjuncts, namely C, is true. By using Mutual Exclusion, we can prove that B is therefore false. 5. ~B 2,4 Mutual Exclusion Now let's look at premise 1. We can apply Modus Tollens here. 6. ~A 1,5 Modus Tollens We have gotten to the conclusion. 1. A > B
