

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 
Disjunctive Addition Disjunctive Addition is a rule of inference pertaining to the OR operator. Disjunctive Addition adds any statement, true or false, to a given true statement. Let's consider a statement "The Moon revolves around the Earth". We know that this statement is true  it is a proven fact. Now that we are given this true statement, we can add any other statement to it by applying Disjunctive Addition. This is how it is done formally: p: "The Moon revolves around the Earth." The given statement p is above the line of dashes, and the new expression p v q formed by applying Disjunctive Addition is below the line. We can also add a statement known to be false to a given true statement: p: "The Moon revolves around the Earth." This is possible because, by definition, Disjunctive Addition can add any statement, true or false, to a given true statement. This is not the extent of the application of Disjunctive Addition. We can add absolutely any statement to a given true statement, even if there does not seem to be a connection between the statements. p: "The Moon revolves around the Earth." This is possible because of the inherent property of the OR operator: A disjunction is true if at least one of its statements is true. Therefore, p v q "The Moon revolves around the Earth or smoking causes lung cancer" is a true statement because we know for a fact that its first part is true  the moon does revolve around the earth. Knowing that, we don't have to worry about the second part ("smoking causes lung cancer")  regardless of whether it is true or not, it is not going to affect the entire statement p v q. In this case, the second part happens to be true  smoking does cause lung cancer, but we might as well have picked any other, true or false, statement.
Other examples of Disjunctive Addition A: "The water is cold."
X: "The painting is extraordinary."
Links to Relevant Problems These are links to validity proof problems whose solutions contain Disjunctive Addition.
