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.
Statement 2 is invalid. Just because John studied for the test does not mean
he actually received an A+. He may have only received a B, or perhaps he
even failed. To take statement 2 as true is to make an error known as a
Mistaken ReversalTM. We use this name because the attempted inference
looks like the reverse of the original statement:
Sufficient Necessary
Study J A+ J
The form here reverses the Study and A+ elements, and although this
statement might be true, it is not definitely true. Just because the necessary
condition has been fulfilled does not mean that the sufficient condition
must occur.
Because the contrapositive both reverses and negates, it is a combination of
a Mistaken Reversal and Mistaken Negation. Since the contrapositive is
valid, it is as if two wrongs do make a right.
A contrapositive denies the necessary condition, thereby making it impossible for
the sufficient condition to occur. Contrapositives can often yield important
insights into a game.
Statement 3 is also invalid. Just because John did not receive an A+ does
not mean he did not study. He may have studied but did not happen to
receive an A+. Perhaps he received a B instead. To take this statement as
true is to make an error known as a Mistaken NegationTM.
Sufficient Necessary
A+ J Study J
The form here negates the A+ and Study elements (this is represented by
the slash through each term), and although this statement might be true, it
is not definitely true. Just because the sufficient condition has not been fulfilled does not mean that the necessary condition cannot occur.
Statement 4 is valid. If studying is the necessary condition for getting an
A+, and John did not study, then according to the original statement there
is no way John could have received an A+. This inference is known as the
contrapositive, and you can see that when the necessary condition fails to
occur, then the sufficient condition cannot occur.
Sufficient Necessary
Study J A+ J
The form here reverses and negates the Study and A+ elements. When you
are looking to find the contrapositive, do not think about the elements and
what they represent. Instead, simply reverse and negate the two terms.
There is a contrapositive for every conditional statement, and if the initial
statement is true, then the contrapositive is also true. The contrapositive is
simply a different way of expressing the initial statement. To analogize, it
is like examining a penny: both sides look different but intrinsically the
value is the same.
These four valid and invalid inferences are used by the test makers to test your
knowledge of what follows from a given statement. Sometimes you will need
to recognize that the contrapositive is present in order to identify a correct
answer, other times you made need to recognize a Mistaken Reversal in order
to avoid a wrong answer, or that an argument is using a Mistaken Negation,
and so forth. When you analyze a conditional statement, you simply need to be
aware that these types of statements exist. At first that will require you to
actively think about the possibilities and this will slow you down, but as time
goes by this recognition will become second nature and you will begin to
solve certain questions extraordinarily fast.
One word of warning: many people read the analysis of valid and invalid
statements and ignore the discussion of the form of the relationships (reversal
of the terms, negation of the terms, etc.). This is very dangerous because it
forces them to rely on their knowledge of the grading system to understand
why each statement is valid or invalid, and if their perception differs from that
of the author, they make mistakes. At first, it is difficult to avoid doing this,
but as time goes on, focus more on the form of the relationship and less on the
content. If you simply try to think through the content of the relationship, you
will likely be at a loss when faced with a conditional relationship involving,
for example, the hemolymph of arthropods.
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.
Statement 2 is invalid. Just because John studied for the test does not mean
he actually received an A+. He may have only received a B, or perhaps he
even failed. To take statement 2 as true is to make an error known as a
Mistaken ReversalTM. We use this name because the attempted inference
looks like the reverse of the original statement:
Sufficient Necessary
Study J A+ J
The form here reverses the Study and A+ elements, and although this
statement might be true, it is not definitely true. Just because the necessary
condition has been fulfilled does not mean that the sufficient condition
must occur.
Because the contrapositive both reverses and negates, it is a combination of
a Mistaken Reversal and Mistaken Negation. Since the contrapositive is
valid, it is as if two wrongs do make a right.
A contrapositive denies the necessary condition, thereby making it impossible for
the sufficient condition to occur. Contrapositives can often yield important
insights into a game.
Statement 3 is also invalid. Just because John did not receive an A+ does
not mean he did not study. He may have studied but did not happen to
receive an A+. Perhaps he received a B instead. To take this statement as
true is to make an error known as a Mistaken NegationTM.
Sufficient Necessary
A+ J Study J
The form here negates the A+ and Study elements (this is represented by
the slash through each term), and although this statement might be true, it
is not definitely true. Just because the sufficient condition has not been fulfilled does not mean that the necessary condition cannot occur.
Statement 4 is valid. If studying is the necessary condition for getting an
A+, and John did not study, then according to the original statement there
is no way John could have received an A+. This inference is known as the
contrapositive, and you can see that when the necessary condition fails to
occur, then the sufficient condition cannot occur.
Sufficient Necessary
Study J A+ J
The form here reverses and negates the Study and A+ elements. When you
are looking to find the contrapositive, do not think about the elements and
what they represent. Instead, simply reverse and negate the two terms.
There is a contrapositive for every conditional statement, and if the initial
statement is true, then the contrapositive is also true. The contrapositive is
simply a different way of expressing the initial statement. To analogize, it
is like examining a penny: both sides look different but intrinsically the
value is the same.
These four valid and invalid inferences are used by the test makers to test your
knowledge of what follows from a given statement. Sometimes you will need
to recognize that the contrapositive is present in order to identify a correct
answer, other times you made need to recognize a Mistaken Reversal in order
to avoid a wrong answer, or that an argument is using a Mistaken Negation,
and so forth. When you analyze a conditional statement, you simply need to be
aware that these types of statements exist. At first that will require you to
actively think about the possibilities and this will slow you down, but as time
goes by this recognition will become second nature and you will begin to
solve certain questions extraordinarily fast.
One word of warning: many people read the analysis of valid and invalid
statements and ignore the discussion of the form of the relationships (reversal
of the terms, negation of the terms, etc.). This is very dangerous because it
forces them to rely on their knowledge of the grading system to understand
why each statement is valid or invalid, and if their perception differs from that
of the author, they make mistakes. At first, it is difficult to avoid doing this,
but as time goes on, focus more on the form of the relationship and less on the
content. If you simply try to think through the content of the relationship, you
will likely be at a loss when faced with a conditional relationship involving,
for example, the hemolymph of arthropods.
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