Negating statements largely consists of adding a “not” if a negative is not present in
the sentence, or removing a “not” if a negative is present. In the disucussion of
Assumptions in Chapter Nine we will discuss statement negation in more detail.
As you diagram each conditional statement, you will face a decision about
how to represent each element of the relationship. Because writing out the
entire condition would be onerous, the best approach is to use a symbol to
represent each condition. For example, we have already used “A+” to represent
the idea of “If someone gets an A+ on a test.” The choice of symbol is yours,
and different students will choose different representations. For example, to
represent “they must have studied for the test,” you could choose “Study” or
the more efficient “S.” Whatever you decide to choose, the symbolization must
make sense to you and it must be clear. For example, if faced with
diagramming a sentence such as, “If you study, then you will be successful,”
you would not want to choose “S” to represent each term as that would be
confusing. A better choice would be “St” for “Study” and “Su” for
“Successful.” Regardless of how you choose to diagram an element, once you
use a certain representation within a problem, stick with that representation
throughout the duration of the question.
As briefly discussed above, negatives can be diagrammed as slashes. Thus,
when faced with a negative term such as “John did not receive an A+,” we
diagram the term as:
A+
Some students ask if they can simply put an “N” in front of the A+ to
represent the “not” or negative idea (as in NA+). We do not recommend this
approach because if that term is later negated by some other part of the
stimulus, you will have a diagram that contains two negatives:
NA+
Because the two negatives translate into a positive (A+), a better approach is to
diagram any negative with a slash, because when the slash is removed the term
returns to “clear” or “positive” status. For those of you also using the Logic
Games Bible, this approach integrates seamlessly with the PowerScore games
diagramming method.
In considering the form of the statements, the position of the slashes is
irrelevant when determining if you are looking at a Repeat, Contrapositive,
Mistaken Reversal, or Mistaken Negation. Consider the following two pairs of
statements, both of which contain contrapositives:
First Pair:
Sufficient Necessary
Original statement: A B
Contrapositive: B A
Second Pair:
Sufficient Necessary
Original statement: C D
Contrapositive: D C
In each pair, the second statement is a contrapositive, and in each
contrapositive the terms are both reversed and negated. Thus, even though the
slashes may be in different places (or nonexistent) in each of the original
statements, both can yield a contrapositive. The form determines the result.
the sentence, or removing a “not” if a negative is present. In the disucussion of
Assumptions in Chapter Nine we will discuss statement negation in more detail.
As you diagram each conditional statement, you will face a decision about
how to represent each element of the relationship. Because writing out the
entire condition would be onerous, the best approach is to use a symbol to
represent each condition. For example, we have already used “A+” to represent
the idea of “If someone gets an A+ on a test.” The choice of symbol is yours,
and different students will choose different representations. For example, to
represent “they must have studied for the test,” you could choose “Study” or
the more efficient “S.” Whatever you decide to choose, the symbolization must
make sense to you and it must be clear. For example, if faced with
diagramming a sentence such as, “If you study, then you will be successful,”
you would not want to choose “S” to represent each term as that would be
confusing. A better choice would be “St” for “Study” and “Su” for
“Successful.” Regardless of how you choose to diagram an element, once you
use a certain representation within a problem, stick with that representation
throughout the duration of the question.
As briefly discussed above, negatives can be diagrammed as slashes. Thus,
when faced with a negative term such as “John did not receive an A+,” we
diagram the term as:
Some students ask if they can simply put an “N” in front of the A+ to
represent the “not” or negative idea (as in NA+). We do not recommend this
approach because if that term is later negated by some other part of the
stimulus, you will have a diagram that contains two negatives:
Because the two negatives translate into a positive (A+), a better approach is to
diagram any negative with a slash, because when the slash is removed the term
returns to “clear” or “positive” status. For those of you also using the Logic
Games Bible, this approach integrates seamlessly with the PowerScore games
diagramming method.
In considering the form of the statements, the position of the slashes is
irrelevant when determining if you are looking at a Repeat, Contrapositive,
Mistaken Reversal, or Mistaken Negation. Consider the following two pairs of
statements, both of which contain contrapositives:
First Pair:
Sufficient Necessary
Original statement: A B
Contrapositive:
Second Pair:
Sufficient Necessary
Original statement: C
Contrapositive: D
In each pair, the second statement is a contrapositive, and in each
contrapositive the terms are both reversed and negated. Thus, even though the
slashes may be in different places (or nonexistent) in each of the original
statements, both can yield a contrapositive. The form determines the result.
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