About Matching Definitions
A matching definitions question names a term and offers four meanings, of which exactly one is the meaning of that term. It is knowledge rather than method, and the marks it carries are for having met the vocabulary of reasoning and method before the paper. What can be practised is the way the questions fail: the three options that are not the answer are not nonsense, they are the meanings of neighbouring terms.
What you need to understand
- The vocabulary is the vocabulary of reasoning and of method: premise, conclusion, inference, assumption, evidence, deduction, induction, abduction, syllogism, fallacy, axiom, theorem, corollary, lemma, conjecture, hypothesis, counterexample, contradiction and paradox.
- A second family comes from handling evidence: sample, bias, correlation, causation, variable, control, reliability, validity, average, median, mode, range and percentile.
- A third comes from deciding: probability, odds, risk, opportunity cost, trade-off, incentive, equilibrium, threshold, feedback and iteration.
- Many of the terms come in opposed pairs, and learning them as pairs halves the work: deduction against induction, correlation against causation, necessary against sufficient, valid against sound, mean against median.
- An option that is not the answer is almost always the definition of a term that sits next to the one asked about, so the question cannot be answered by asking which option sounds sensible. It is answered by asking which term each option belongs to.
- A definition states what is necessary and sufficient. An example of the term, or something merely associated with it, is not a definition however true the statement is.
- Almost every definition in this vocabulary has the shape of a kind and a difference: a thing of a certain kind that does a certain job. An option that gives only the kind is too broad; an option that adds a condition the thing need not have is too narrow.
- Several of these words carry a narrow technical sense and a loose everyday sense, and the everyday sense is what the wrong options are written in. Theory does not mean a guess, proof does not mean evidence, significant does not mean important, and risk is not the same as uncertainty.
- Where two options both seem to fit, the fault is nearly always scope, and the way to find it is to test the option that looks too broad by naming something that fits the option but is not the term.
- The same technique answers the negative form, which asks which option is NOT the definition of the term. The three that fit identify the answer to be rejected, so it is usually quicker than the positive form.
- A variant gives a single sentence with a blank and four terms to fill it. Then the option has to satisfy the grammar of the sentence as well as the meaning, which is often what decides between two candidates.
- Reading the options before the term is sometimes the faster order, because a term you know well turns the question into finding one option rather than judging four.
- These questions are usually written to a table of terms rather than invented one at a time, which is why the options are so close to each other and why a term you half know is more dangerous than one you do not know at all.
How to work through these questions
- Read the term and say its meaning to yourself before looking at the options. You are then matching one meaning against four candidates rather than choosing among four.
- If no meaning comes, read the options and name the term each one belongs to. The one left unclaimed when the named terms are struck out is the answer.
- When two options are close, test scope rather than wording: name a thing that fits the option but is not the term. If one exists, the option is too broad.
- Use the oppositions in the vocabulary. If an option describes reasoning from particular cases to a general rule, the term cannot be deduction, whatever else the option says.
- Prefer the option that says what the thing does over one that says how it is usually recorded or written, because the second is an accompaniment and only the first is the definition.
- Do not choose on appearance. Options are written to be of comparable length and form, so length and technical phrasing carry no information.
Mistakes that cost marks
- Choosing an example of the term instead of its definition. A statement can be entirely true of the term and still not be what the term means.
- Choosing an option that is true of a wider class. An animal that flies is not a definition of a bird.
- Choosing an option that adds a condition the thing need not satisfy. An argument that is written down is not a definition of an argument.
- Reading a term in its everyday sense when the technical sense is narrower, which is exactly what the wrong options are built on.
- Mistaking a method or instrument associated with the thing for part of its definition, as with tests and their significance levels.
- Accepting an option that restates the term in other words and so says nothing.
- Assuming that the longest or most formal option is the right one, which is a habit that costs marks in both directions.
- In the negative form, losing the negation in the last few seconds and choosing a definition that fits.
Worked example
Which of these is the definition of the term "lemma"?
- Say the meaning before reading the options. A lemma is a small result proved on the way to something larger.
- Then name the term each option belongs to rather than judging how sensible it sounds. Option A, a statement proved from axioms and from results already proved, is the definition of a theorem.
- Option B, an exchange in which something is gained by giving something else up, is the definition of a trade-off.
- Option C, repeating a procedure so that each round builds on the one before it, is the definition of iteration.
- Option D, a minor result proved on the way to a more important one, is the only one left and is the definition of a lemma.
Answer: A lemma is a minor result proved on the way to a more important one
Practice questions with answers
A few Matching Definitions questions with the full solution shown, so you can see
how the method is applied before you attempt the timed set.
Question 1
Which of these is the definition of the term "lemma"?
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A
a statement proved from axioms and from results already proved
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B
an exchange in which something is gained by giving something else up
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C
repeating a procedure so that each round builds on the one before it
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D
a minor result proved on the way to a more important one
Answer: Option D — with explanation
The term is lemma, and it means a minor result proved on the way to a more important one.
A question of this kind is answered by knowing the terms rather than by reasoning from them, so the useful move is to be sure of each option as it is read. The three that are not the answer are the meanings of other terms in the same vocabulary, which is what makes them difficult to dismiss without knowing them:
- "iteration" means repeating a procedure so that each round builds on the one before it
- "theorem" means a statement proved from axioms and from results already proved
- "trade-off" means an exchange in which something is gained by giving something else up
Common mistakes
- this is the meaning of "theorem", not of "lemma"
- this is the meaning of "trade-off", not of "lemma"
- this is the meaning of "iteration", not of "lemma"
Question 2
Which of these is what "validity" means?
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A
a statement accepted without proof because it is the starting point of a system
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B
the extent to which a test measures what it claims to be measuring
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C
a set of statements in which some are offered in support of another
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D
an exchange in which something is gained by giving something else up
Answer: Option B — with explanation
The term is validity, and it means the extent to which a test measures what it claims to be measuring.
A question of this kind is answered by knowing the terms rather than by reasoning from them, so the useful move is to be sure of each option as it is read. The three that are not the answer are the meanings of other terms in the same vocabulary, which is what makes them difficult to dismiss without knowing them:
- "argument" means a set of statements in which some are offered in support of another
- "axiom" means a statement accepted without proof because it is the starting point of a system
- "trade-off" means an exchange in which something is gained by giving something else up
Common mistakes
- this is the meaning of "trade-off", not of "validity"
- this is the meaning of "argument", not of "validity"
- this is the meaning of "axiom", not of "validity"
Question 3
Which of these gives the meaning of the term "induction"?
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A
a single case that shows a general claim to be false
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B
choosing the best available option within the constraints that apply
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C
reasoning that generalises from particular cases to a wider claim
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D
two statements that cannot both be true at the same time
Answer: Option C — with explanation
The term is induction, and it means reasoning that generalises from particular cases to a wider claim.
A question of this kind is answered by knowing the terms rather than by reasoning from them, so the useful move is to be sure of each option as it is read. The three that are not the answer are the meanings of other terms in the same vocabulary, which is what makes them difficult to dismiss without knowing them:
- "optimisation" means choosing the best available option within the constraints that apply
- "contradiction" means two statements that cannot both be true at the same time
- "counterexample" means a single case that shows a general claim to be false
Common mistakes
- this is the meaning of "counterexample", not of "induction": a single case that shows a general claim to be false
- this is the meaning of "contradiction", not of "induction": two statements that cannot both be true at the same time
- this is the meaning of "optimisation", not of "induction"
Question 4
Which of these is what "average" means?
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A
a statement believed to be true but not yet proved
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B
a single value chosen to represent the middle of a set of values
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C
two statements that cannot both be true at the same time
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D
the extent to which a measurement gives the same result when repeated
Answer: Option B — with explanation
The term is average, and it means a single value chosen to represent the middle of a set of values.
A question of this kind is answered by knowing the terms rather than by reasoning from them, so the useful move is to be sure of each option as it is read. The three that are not the answer are the meanings of other terms in the same vocabulary, which is what makes them difficult to dismiss without knowing them:
- "conjecture" means a statement believed to be true but not yet proved
- "reliability" means the extent to which a measurement gives the same result when repeated
- "contradiction" means two statements that cannot both be true at the same time
Common mistakes
- this is the meaning of "contradiction", not of "average": two statements that cannot both be true at the same time
- this is the meaning of "conjecture", not of "average": a statement believed to be true but not yet proved
- this is the meaning of "reliability", not of "average"
Question 5
Which of these is what "percentile" means?
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A
the value below which a given proportion of a set of values falls
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B
reasoning in which the conclusion must be true if the premises are true
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C
a reward or a penalty that makes a course of action more or less attractive
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D
the extent to which a test measures what it claims to be measuring
Answer: Option A — with explanation
The term is percentile, and it means the value below which a given proportion of a set of values falls.
A question of this kind is answered by knowing the terms rather than by reasoning from them, so the useful move is to be sure of each option as it is read. The three that are not the answer are the meanings of other terms in the same vocabulary, which is what makes them difficult to dismiss without knowing them:
- "incentive" means a reward or a penalty that makes a course of action more or less attractive
- "deduction" means reasoning in which the conclusion must be true if the premises are true
- "validity" means the extent to which a test measures what it claims to be measuring
Common mistakes
- this is the meaning of "deduction", not of "percentile"
- this is the meaning of "incentive", not of "percentile"
- this is the meaning of "validity", not of "percentile"
Frequently asked questions
Is this not simply a vocabulary test?
It is, and that is both its weakness and the reason it is worth ten minutes of preparation. The vocabulary it tests is the vocabulary in which every other reasoning question is written, so a candidate who has learned these terms reads the rest of the paper more accurately.
How many terms do I need to know?
The same few dozen recur across papers, and a list of about sixty covers most of what is asked. Learning them as opposed pairs rather than as a list is the quicker route.
What should I do when two options both seem right?
Test scope. Name something that fits the option you suspect but is not the term; if you can, the option is too broad. If the option adds a condition the term does not need, it is too narrow. The definition is the option that is exactly the right width.
Should I learn the definitions word for word?
No. Learn the shape, which is a thing of a certain kind that does a certain job, and learn which term each neighbouring definition belongs to. Word for word learning fails the moment the paper words the option differently, which it always does.
How is this different from the essential part topic?
Essential part asks what a thing cannot be without, while this asks what a word means. The way the two are failed is the same, and so is the cure: tell the necessary and sufficient condition from an example, an association, or a wider class.
