When one thing is a requirement for another to happen, we call the first a necessary condition for the second. An example is having gas in order for a car to run. There are various ways of expressing this relationship: We could say that one thing is true only if the other is true (a car runs only if it has gas) or we could say that the first is not true unless the other is true (a car will not run unless it has gas).

In standard form, we can restate the relationship so that we hear a sufficient condition ("If a car runs then it has gas," which is equivalent to the contrapositive statement that "If the car does not have gas then it does not run").

Other ways of expressing the same relationship in the example would be: "In order for a car to run it has to have gas."
"Having gas is essential for a car to run."
"To have a car running calls for it have gas."

A key logical rule that plays on the contrapositive relationship is that denying the consequent (modus tollens) implies denying the antecedent. We make use of this pattern in PLN derivations by first converting a conditional to its contrapositive, then using the modus ponens pattern. For example, given PQC and QN, we restate PQC as QNPNC, then derive PN.

The corresponding fallacy is denying the antecedent--incorrectly reasoning that a false consequent follows from a false antecedent (as when we might think that, given Jane will pass if she studies, she will not pass because she is not studying.

For additional practice run the program STDFORM that comes on your disk.

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