Sufficient and Necessary Conditions

In the diagram of a conditional statement, the sufficient condition always
comes at the “beginning” of the arrow, and the necessary condition always
comes at the “end” of the arrow. Thus, when a sufficient condition occurs,
you can follow the arrow to the necessary condition.
Conditional reasoning is a fundamental component of both the Logical
Reasoning and Logic Games sections of the LSAT. If you have already read
the PowerScore LSAT Logic Games Bible, then you have encountered basic
conditional reasoning. In this chapter we will further explore the concept.
Conditional reasoning is the broad name given to logical relationships
composed of sufficient and necessary conditions. Any conditional statement
consists of at least one sufficient condition and one necessary condition. Let us
begin by defining each condition:
A sufficient condition can be defined as an event or circumstance
whose occurrence indicates that a necessary condition must also occur.
A necessary condition can be defined as an event or circumstance
whose occurrence is required in order for a sufficient condition to
occur.
Now, let’s try that in English! In other words, if a sufficient condition occurs,
you automatically know that the necessary condition also occurs. If a
necessary condition occurs, then it is possible but not certain that the sufficient
condition will occur.
In everyday use, conditional statements are often brought up using the
“if...then” construction. Consider the following statement, which we will use
for the majority of our discussion:
If someone gets an A+ on a test, then they must have studied for the
test.
If the above statement is true, then anyone who receives an A+ on a test must
have studied for the test. Anyone who studied might have received an A+, but
it is not guaranteed. Since getting an A+ automatically indicates that studying
must have occurred, the sufficient condition is “get an A+” and it follows that
“must have studied” is the necessary condition.
In the real world, we know that a statement such as the above is usually true,
but not always. There could be a variety of other ways to get an A+ without
studying, including cheating on the test, bribing the teacher for a higher grade,
or even breaking into the school computer system and changing the grade.
However, in the LSAT world, when an author makes a conditional statement,
Conditional reasoning is one of the pillars of the LSAT, and appears in a large
number of problems.
Conditional reasoning can occur in any question type.
116 The PowerScore LSAT Logical Reasoning
he or she believes that statement to be true without exception. So, if the
statement above is made in the LSAT world, then according to the author
anyone who gets an A+ must have studied.
To efficiently manage the information in conditional statements, we use arrow
diagrams. For a basic conditional relationship, the arrow diagram has three
parts: a representation of the sufficient condition, a representation of the
necessary condition, and an arrow pointing from the sufficient condition to the
necessary condition. Most often, this arrow points from left to right
(exceptions will be discussed in the chapter on Formal Logic).
The diagram for the previously discussed statement would be as follows:
Sufficient                  Necessary
A+                       Study