The Unless EquationTM

To diagram a statement that contains “unless,” convert the variable modified by
“unless” into the necessary condition. Take the remainder, negate it, and
convert it into the sufficient condition. The same technique applies to statements that
contain “until,” “except,” and “without.”
In the case of “unless,” “except,” “until,” and “without,” a special two-step
process called the Unless Equation is applied to the diagram:
1. Whatever term is modified by “unless,” “except,” “until,” or “without”
becomes the necessary condition.
2. The remaining term is negated and becomes the sufficient condition.
For example, consider the following:
Unless a person studies, he or she will not receive an A+.
Since “unless” modifies “a person studies,” “Study” becomes the necessary
condition. The remainder, “he or she will not receive an A+,” is negated by
dropping the “not” and becomes “he or she will receive an A+.” Thus, the
sufficient condition is “A+,” and the diagram is as follows:
Sufficient                  Necessary
A+                        Study
Here is another example:
There can be no peace without justice.
Apply the Unless Equation”
1. Since “without” modifies “justice,” “justice” becomes the necessary
condition and we represent this with a “J.”
2. The remainder, “There can be no peace ,” is negated by dropping the
“no,” and becomes the sufficient condition “P.”
The diagram is as follows:
Sufficient                      Necessary
P                              J
Thus, if peace occurs, there must be justice.