Negating Conditional Statements

To logically negate a conditional statement,
negate the necessary condition.
To negate a conditional statement you must show that the necessary condition is
not in fact necessary. For example, “To be rich, you must be smart” becomes
“To be rich, you do not necessarily have to be smart.” Assumption question
answer choices containing conditional answer choices occur frequently on the
LSAT and you must understand how to properly negate them.
It is also worth noting that the logical negation of a conditional statement is
different than the Mistaken Negation of that statement. The Mistaken Negation
is a failed inference that follows from negating both sides of the statement. A
logical negation negates just the necessary condition in an attempt to produce
the opposite of the statement. Example:
Original Statement: If A occurs, then B occurs.
Diagram: A-----------> B
Logical Negation: A-----------> B
Mistaken Negation: A-----------> B

Valid and Invalid Statements

Conditional reasoning occurs when a statement containing sufficient and
necessary conditions is used to draw a conclusion based on the statement.
Although the discussion example may seem relatively easy, the makers of the
LSAT often use conditional reasoning to ensnare unwary test takers, especially
in the Logical Reasoning section. When analyzing a basic conditional
statement, there are certain observations that can be inferred from the
statement and there are observations that may appear true but are not certain.
Taking our discussion example as undeniably true, consider the following four
statements:
1. John received an A+ on the test, so he must have studied for the test.
2. John studied for the test, so he must have received an A+ on the test.
3. John did not receive an A+ on the test, so he must not have studied on
the test.
4. John did not study for the test, so he must not have received an A+ on
the test.
Two of the four statements above are valid, and two of the four statements are
invalid. Can you identify which two are valid? The answers are on the next
page.
The Repeat form simply restates the elements in the original order they appeared.
This creates a valid inference.
A Mistaken Reversal switches the elements in the sufficient and necessary conditions,
creating a statement that does not have to be true.
A Mistaken Negation negates both conditions, creating a statement that
does not have to be true.
Statement 1 is valid. According to the original statement, because John
received an A+, he must have studied for the test. We call this type of
inference the Repeat form because the statement basically repeats the parts
of the original statement and applies them to the individual in question,
John.
We would use the following diagram for statement 1:
Sufficient Necessary
A+ J Study J
Note how the A+ and Study elements are in the same position as our
original statement, hence the “Repeat” form moniker. The “J” subscript
represents “John.” John is not a separate diagramming element because
John is simply someone experiencing the conditions in the statement.