Disjunctive Infer. (XOR)
5-step or more
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
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
Links to Relevant Problems
These are links to validity proof problems whose solutions contain the Chain Rule.