

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 
Chain Rule The Chain Rule is a rule of inference pertaining to the IF/THEN operator. The Chain Rule is used to combine two conditionals of the form p > q and q > r into p > r. Imagine we are given two conditionals, p > q and q > r: p > q: "If Jane leaves home late, she will miss her train." Now let's consider the second conditional, q > r. Note that it contains the same letter that we used in the first conditional, namely q. This means that q has to remain the same as in the first conditional. q > r: "If Jane misses her train, she will be late for work." Given the two conditionals, It is perfectly natural for us to say: "If Jane leaves home late, she will be late for work." That is how the Chain Rule works. Formally, we would write p > q: "If Jane leaves home late, she will miss her
train." The given conditionals are above the line of dashes, and the new expression p > r formed by applying the Chain Rule is below the line.
Other examples of the Chain Rule W > M: "If you have a job, you will get money."
X > Y: "If you read the book, you're ready for the
exam."
Links to Relevant Problems These are links to validity proof problems whose solutions contain the Chain Rule.
