

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 (Bad Argument) The problems below contain a bad argument. That means that the conclusion given in the problem is wrong, and we have to prove it.
Problem 1 1. E > F Looking at premises 1 and 2, we realize that we can apply Modus Tollens here. 3. ~E 1,2 Modus Tollens The result, however, contradicts the conclusion (E). The conclusion is invalid; therefore, we have an invalid argument. 1. E > F
Problem 2 1. G > H If we look at premises 1 and 4, we see that the Chain Rule can be applied right away. 5. G > ~K 1,4 Chain Rule We know that we eventually have to get to L. There is only one premise containing L: it's premise 3. If we apply Contrapositive to it, we bring ~K to the front, in which case we can use it later together with the result of step 5. 6. ~K > ~L 3 Contrapositive Now we can apply the Chain Rule again. 7. G > ~L 5,6 Chain Rule In this conditional, ~L is true when G is true. We can extract G from a conjunctive in premise 2 using Simplification: 8. G 3 Simplification Finally we prove that ~L is true, L is false, and the argument is invalid by Modus Ponens. 9. ~L 8,9 Modus Ponens Let's retrace our step. 1. G > H
