Some TOEFL inference questions ask about situations that are the opposite of the situations described in the passage. To answer this type of question, you need to use contrapositive. To see how it is used, let's look at this question:
Question (hard)
One of the most popular techniques to study infant perception is the habituation-dishabituation method. In this technique, a single stimulus is presented repeatedly to the infant until there is a measurable decline (habituation) in whatever attending behavior is being observed. At that point a new stimulus is presented, and any recovery (dishabituation) in responsiveness is recorded. If the infant fails to dishabituate and continues to show habituation with the new stimulus, it is believed that the baby is unable to perceive the new stimulus as different. The habituation-dishabituation paradigm has been used most extensively with studies of auditory and olfactory perception in infants.
Based on the passage, what can we infer if infants are believed to be able to differentiate between stimuli in a habituation-dishabituation study?
Dishabituation occurs with the introduction of a new stimulus.
Electrical responses in the infant’s brain decline with each new stimulus.
Habituation is continued with the introduction of a new stimulus.
The infant displays little change in electrical brain responses.
This is a difficult question because the passage itself is difficult to understand and does not mention what the question is asking about: “is able to differentiate.” The only information relating to the question is the opposite situation, "is unable to perceive the new stimulus as different." which, however, does not seem helpful. However, this question can be answered without difficulty if you know the logical relationship called contrapositive.
TOEFL Reading Self-study Course
Contrapositive
In logic and mathematics, “if not Q, then not P” is called the contrapositive of “If P then Q.” That is, the contrapositive reverses the conditions of the original statement and then negates them. This holds:
“If P, then Q” is logically equivalent to “if not Q, then not P.”
If P, then Q = if not Q, then not P
For example,
If there is smoke, there is fire
= if there is no fire, there is no smoke.
If John studies for the test, he will get a good grade
= If John doesn't get a good grade, then he didn't study for the test.
The “if… then” statement can be expressed with other phrases like all, when, and whenever.
All red objects have color
= If an object is red, then it has color
= If an object does not have color, then it is not red
All quadrilaterals have four sides
= If a polygon is a quadrilateral, then it has four sides
If a polygon does not have four sides, then it is not a quadrilateral
The contrapositive relationship of statements is very useful to answer TOEFL inference questions. The relevant sentence in the passage describes a certain situation in terms of ‘if P, then Q,’ and the question asks you to infer something about the situation where Q is not true. The correct option should be that P is not true. For example, this is given:
When baby birds are hungry, parent birds feed them.
The question then asks “When birds do not feed their nestlings?” Using the contrapositive, we know that the answer is “when baby birds are not hungry.”
Now that we understand how to use contrapositive, let’s examine TOEFL questions that ask you to use contrapositive.
Question (hard)
What benefit do begging nestlings derive from their communications? One hypothesis is that a noisy baby bird provides accurate signals of its real hunger and good health, making it worthwhile for the listening parent to give it food in a nest where several other offspring are usually available to be fed. If parent birds use begging intensity to direct food to healthy offspring capable of vigorous begging, then parents should make food delivery decisions on the basis of their offspring's calls. Indeed, if you take baby tree swallows out of a nest for an hour feeding half the set and starving the other half, when the birds are replaced in the nest, the starved youngsters beg more loudly than the fed birds, and the parent birds feed the active beggars more than those who beg less vigorously.
Based on the passage, we can infer that birds do not feed their offspring if?
baby birds are just fed.
baby birds are out of their nest.
baby birds do not beg.
baby birds are unhealthy or full.
Analysis
According to the passage,
a noisy baby bird provides accurate signals of its real hunger and good health, making it worthwhile for the listening parent to give it food
from this we know these:
a noisy baby bird = a hungry and healthy baby (given)
if a baby bird is noisy, then the parent gives it food (given)
if a baby bird is hungry and healthy, then the parent gives it food (1 and 2, identity substitution)
If the parent does not feed a baby bird, the baby is not (healthy and hungry) (contrapositive of 3)
not (healthy and hungry) = not healthy or not hungry (De Morgan's law: you should have learned this law in an algebra class)
The question tests your ability to identify the contrapositive of the original sentence. D is the contrapositive. To tackle this type, you first simplify the idea in the passage with a “if then” conditional sentence, and then find the contrapositive.
A is a trap. A looks tempting, but A is not supported by the passage.
B is something mentioned in the passage, but a red herring.
C is another trap.
D is logically inferred from the passage.
Answer: D
Question (hard)
One of the most popular techniques to study infant perception is the habituation-dishabituation method. In this technique, a single stimulus is presented repeatedly to the infant until there is a measurable decline (habituation) in whatever attending behavior is being observed. At that point a new stimulus is presented, and any recovery (dishabituation) in responsiveness is recorded. If the infant fails to dishabituate and continues to show habituation with the new stimulus, it is believed that the baby is unable to perceive the new stimulus as different. The habituation-dishabituation paradigm has been used most extensively with studies of auditory and olfactory perception in infants.
Based on the passage, what can we infer if infants are believed to be able to differentiate between stimuli in a habituation-dishabituation study?
Dishabituation occurs with the introduction of a new stimulus.
Electrical responses in the infant’s brain decline with each new stimulus.
Habituation is continued with the introduction of a new stimulus.
The infant displays little change in electrical brain responses.
Analysis
Since the question contains “infants are able to differentiate between stimuli,” we need to look for sentences that talk about when infants are able to differentiate between stimuli. The only relevant sentence is this:
If the infant fails to dishabituate and continues to show habituation with the new stimulus, it is believed that the baby is unable to perceive the new stimulus as different.
This clue sentence describes the opposite situation.:
P = the infant fails to dishabituate (fail to dishabituate = continue to show habituation with the new stimulus)
Q = it is believed that the baby is unable to perceive the new stimulus as different.
So this is the contrapositive of the previous sentence:
If it is believed that the baby is able to perceive the new stimulus as different, then the baby does not fail ( = succeed) to dishabituate.
So the answer must be dishabituation.
A is what we are booking for.
B is irrelevant.
C is the opposite situation, that is, infants are unable to differentiate, and so is false.
D is irrelevant.
Answer: A
TOEFL Reading Self-study Course
Moral of the story:
When you see a question that asks for the opposite of what is mentioned in the passage, the correct answer is the opposite of the conditional phrase (antecedent, the if-clause). Remember this:
